PrepScholar Sat Practice Test 3 Answers
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Transcript of PrepScholar Sat Practice Test 3 Answers
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 140
Answer ExplanationsSAT
reg
Practice Test 3
copy 2015 The College Board College Board SAT and the acorn logo are registered trademarks of the College Board 5LSA08
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 240
1
Answer Explanations
SAT Practice Test 3
Section 1 Reading Test
QUESTION 1
Choice B is the best answer In the passage Lady Carlotta is approachedby the ldquoimposingly attired ladyrdquo Mrs Quabarl while standing at a train sta-
tion (lines 32-35) Mrs Quabarl assumes Lady Carlotta is her new nanny
Miss Hope ldquoYou must be Miss Hope the governess Irsquove come to meetrdquo (lines
36-37) Lady Carlotta does not correct Mrs Quabarlrsquos mistake and replies
ldquoVery well i I must I mustrdquo (line 39)
Choices A C and D are incorrect because the passage is not about a woman
weighing a job choice seeking revenge on an acquaintance or disliking her
new employer
QUESTION 2
Choice C is the best answer In lines 1-3 the narrator states that Lady
Carlotta ldquostepped out on to the platorm o the small wayside station and
took a turn or two up and down its uninteresting lengthrdquo in order to ldquokill
timerdquo In this context Lady Carlotta was taking a ldquoturnrdquo or a short walk
along the platorm while waiting or the train to leave the station
Choices A B and D are incorrect because in this context ldquoturnrdquo does not
mean slight movement change in rotation or course correction While Lady
Carlotta may have had to rotate her body while moving across the station
ldquotook a turnrdquo implies that Lady Carlotta took a short walk along the plat-
ormrsquos length
QUESTION 3
Choice A is the best answer In lines 10-14 the narrator states that some o
Lady Carlottarsquos acquaintances would ofen admonish or criticize Lady Carlotta
or meddling in or openly expressing her opinion on other peoplersquos affairs
Choices B C and D are incorrect because the narrator does not suggest that
other people viewed Lady Carlotta as tactul ambitious or unriendly
7262019 PrepScholar Sat Practice Test 3 Answers
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2
QUESTION 4
Choice A is the best answer In lines 10-14 the narrator states that people
ofen criticized Lady Carlotta and suggested that she not interere in other
peoplersquos affairs which were ldquonone o her businessrdquo Te act that people
ofen were critical o Lady Carlottarsquos behavior provides evidence that Lady
Carlotta was outspoken
Choices B C and D do not provide the best evidence that Lady Carlotta was
outspoken Choices B C and D mention Lady Carlotta but do not speciy
how others view her
QUESTION 5
Choice C is the best answer Te narrator notes that Lady Carlotta decided
not to interere when one o her ldquomost eloquent exponentsrdquo was stuck in a
tree because an angry boar was nearby (lines 14-22) Tis ldquoeloquent expo-
nentrdquo was a woman who ofen criticized Lady Carlotta or interering inother peoplersquos affairs Lady Carlottarsquos decision to ldquoput the doctrine o non-
intererence into practicerdquo (to not help her emale acquaintance who was
ldquobesiegedrdquo in a tree) suggests that Lady Carlotta has a sense o humor
Choices A B and D are incorrect because the description o how she ldquoput
the doctrine o non-intererence into practicerdquo does not suggest that Lady
Carlotta is deceptive or cruel or explain a surprising change in her behavior
QUESTION 6
Choice A is the best answer Te narrator explains that Mrs Quabarl toldLady Carlotta about the ldquonature o the chargerdquo when she gave Lady Carlotta
details about the Quabarl children (line 53-61) Since Lady Carlotta is pre-
tending to be a governess the term ldquochargerdquo reers to her responsibilities or
job duties when caring or the Quabarl children
Choices B C and D are incorrect because in this context ldquochargerdquo does not
mean attack ee or expense
QUESTION 7
Choice A is the best answer Lady Carlotta learns about Mrs Quabarlrsquos chil-dren Claude Wilrid and Irene (lines 53-58) Te narrator then describes
Mrs Quabarlrsquos child Viola as ldquosomething or other else o a mould equally
commonplace among children o that class and type in the twentieth cen-
turyrdquo (lines 58-61) Tis statement about Viola implies that all o the Quabarl
children have skills typical or ldquoo a mould equally commonplacerdquo to other
peers in their social class
Choices B C and D are incorrect because the narrator does not indicate that
all o the Quabarl children are unusually creative and intelligent hostile to
the idea o having a governess or more educated than their peers
7262019 PrepScholar Sat Practice Test 3 Answers
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3
QUESTION 8
Choice B is the best answer In lines 62-69 Mrs Quabarl explains to Lady
Carlotta that she wants her children to actively participate in their education
and that Lady Carlotta should not create lessons that require her children to
simply memorize historical figures and dates Mrs Quabarl emphasizes an
education centered on active engagement when she states that her childrenshould ldquonot only be AUGH but INERESED in what they learnrdquo
Choices A C and D are incorrect because the narrator does not suggest that
Mrs Quabarl avors an education that emphasizes traditional values artistic
experimentation or actual retention
QUESTION 9
Choice B is the best answer In lines 77-82 the narrator describes Mrs
Quabarl as appearing ldquomagnificent and autocraticrdquo or outwardly domineer-
ing but easily ldquocowed and apologeticrdquo when someone challenges or defiesher authority
Choices A C and D are incorrect because the narrator does not describe
Mrs Quabarl as selfish bitter or requently imprudent
QUESTION 10
Choice D is the best answer In lines 77-82 the narrator provides evidence
that Mrs Quabarl appears imposing or autocratic but is easily defied or
opposed ldquoShe was one o those imperectly sel-assured individuals who are
magnificent and autocratic as long as they are not seriously opposed Teleast show o unexpected resistance goes a long way towards rendering them
cowed and apologeticrdquo
Choices A B and C do not provide the best evidence that Mrs Quabarl
appears imposing but is easily defied Choices A and B are incorrect because
they present Mrs Quabarlrsquos opinions on railway companies and educa-
tion and choice C is incorrect because it ocuses on Lady Carlotta not
Mrs Quabarl
QUESTION 11
Choice A is the best answer While the author predominantly supports
the use o public transportation in the third paragraph he recognizes
some limitations to the public transportation system it is a ldquodepressing
experiencerdquo (lines 25-26) and ldquounderunded ill-maintained and
ill-plannedrdquo (line 31)
Choices B C and D are incorrect because the third paragraph does not
expand upon an argument made in the first two paragraphs provide an
overview o a problem or advocate ending the use o public transportation
7262019 PrepScholar Sat Practice Test 3 Answers
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4
QUESTION 12
Choice C is the best answer Te author notes that in North America ldquohopping
in a car almost always gets you to your destination more quicklyrdquo (lines 32-34)
Tis statement suggests that speed is one advantage to driving in North America
Choices A B and D are incorrect because the author does not cite environmen-
tal impact convenience or cost as advantages o driving in North America
QUESTION 13
Choice D is the best answer In lines 32-34 the author provides evidence
that speed is one advantage to driving in North America because driving
ldquoalmost always gets you to your destination more quicklyrdquo
Choices A B and C do not provide the best evidence that speed is one
advantage to driving in North America Choices A and B are incorrect
because they offer general inormation about using public transportationChoice C is incorrect because although these lines mention North America
they ocus on the disadvantages o public transportation
QUESTION 14
Choice B is the best answer Te author argues in the ourth paragraph that
public transportation ldquocan be aster more comortable and cheaper than the
private automobilerdquo (lines 36-37) and provides examples o ast and conve-
nient public transportation systems
Choices A C and D are incorrect because they ocus on points made in theourth paragraph rather than the paragraphrsquos central idea
QUESTION 15
Choice B is the best answer In lines 35-37 the author provides evidence
that some public transportation systems are superior to driving because
public transportation ldquocan be aster more comortable and cheaper than the
private automobilerdquo
Choices A C and D do not provide the best evidence that some public
transportation systems are superior to driving as they highlight points madein the ourth paragraph rather than the paragraphrsquos central idea
QUESTION 16
Choice C is the best answer In the last paragraph the author explains the
trend that people who became adults around the end o the twentieth cen-
tury are more willing to use public transportation than people rom older
generations Te author notes ldquoI you credit the demographers this transit
trend has legsrdquo (lines 58-59) In this context ldquocreditrdquo means to believe the
demographersrsquo claims about the trend
7262019 PrepScholar Sat Practice Test 3 Answers
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5
Choices A B and D are incorrect because in this context ldquocreditrdquo does not
mean endow attribute or honor
QUESTION 17
Choice B is the best answer In lines 59-63 the author explains the trend
o people who became adults around the end o the twentieth centuryldquotend[ing] to avor cities over suburbsrdquo In this context these adults ldquoavorrdquo
or preer cities over suburbs
Choices A C and D are incorrect because in this context ldquoavorrdquo does not
mean indulge resemble or serve
QUESTION 18
Choice B is the best answer In lines 63-67 the author explains that while
riding on public transportation people can use personal electronic devices
such as ldquoiPads MP3 players Kindles and smartphonesrdquo
Choices A C and D are incorrect because they do not show that public
transportation is compatible with the use o personal electronic devices
QUESTION 19
Choice A is the best answer Figure 1 shows that 107 o public transpor-
tation passengers are students and 67 o public transportation passengers
are retirees Tus more students than retirees use public transportation
Choices B and C are incorrect because figure 1 shows that more employedthan unemployed people use public transportation and that more employed
people than homemakers use public transportation Choice D is incorrect
because figure 1 does not explain how requently passengers use public
transportation it only identifies public transportation passengers by their
primary occupation
QUESTION 20
Choice A is the best answer Figure 1 shows that 72 o public transporta-
tion passengers are ldquoemployed outside the homerdquo and figure 2 indicates that
591 o public transportation trips are or ldquoworkrdquo It can be inerred romthese figures that many public transportation passengers take public trans-
portation to their place o employment
Choices B C and D are incorrect because figure 1 and figure 2 do not
indicate that public transportation passengers primarily use the system to
run errands use their own car on weekends or are planning to purchase
a car
7262019 PrepScholar Sat Practice Test 3 Answers
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6
QUESTION 21
Choice D is the best answer Te author explains that Ken Dial created an
experiment to study the evolution o flight by observing how baby Chukars
learn to fly During the experiment Dial noticed the unusual way Chukars
use their ldquolsquowings and legs cooperativelyrsquordquo to scale hay bales (lines 38-43) and
he created ldquoa series o ingenious experimentsrdquo (line 46) to study this obser- vation Afer his additional experiments Dial determined that these baby
birds angle ldquotheir wings differently rom birds in flightrdquo (lines 49-50)
Choices A B and C are incorrect because they do not accurately reflect the
sequence o events in the passage
QUESTION 22
Choice A is the best answer In lines 6-9 the author explains that Dial was
ldquochallengedrdquo or dared by graduate students to develop ldquonew datardquo on a long-
standing scientific debate (the ldquoground-up-tree-downrdquo theory)
Choices B C and D are incorrect because in this context ldquochallengedrdquo does
not mean required disputed with or competed with
QUESTION 23
Choice A is the best answer Te author explains that Dial created his initial
experiment to try and create ldquonew data on the age-old ground-up-tree-down
debaterdquo and that he looked or ldquocluesrdquo in ldquohow baby game birds learned to
flyrdquo (lines 8-11) Te note at the beginning o the passage explains the ldquoage-
old ground-up-tree down debaterdquo and offers two different theories on howbirds evolved to fly Finally the last paragraph o the passage discusses WAIR
in an evolutionary context
Choices B C and D are incorrect because they do not identiy Dialrsquos central
assumption in setting up his research
QUESTION 24
Choice B is the best answer In lines 6-11 the author provides evidence that
Dialrsquos central assumption in setting up his research is that the acquisition o
flight in young birds is linked to the acquisition o flight in their ancestorsTe author notes that Dial created a project to ldquocome up with new data on
the age-old ground-up-tree-down debaterdquo
Choices A C and D do not provide the best evidence that Dialrsquos central
assumption in setting up his research is that the acquisition o flight in young
birds is linked to the acquisition o flight in their ancestors Choices A C
and D are incorrect because they ocus on Dialrsquos experiment and his obser-
vations on ground birds
7262019 PrepScholar Sat Practice Test 3 Answers
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7
QUESTION 25
Choice C is the best answer When a rancher observed Dialrsquos laboratory
setup he was ldquoincredulousrdquo that the Chukars were living on the ground and
he advised Dial to give the birds ldquosomething to climb onrdquo (lines 16-23) Tis
ldquokey piece o advicerdquo (line 14) led Dial to add hay bales to his laboratory
Dial later noticed that the Chukars were using their legs and wings to scalethe hay bales and this observation became the ocal point o his research
Choices A B and D are incorrect because the incident with the local rancher
did not serve to reveal Dialrsquos motivation or creating the project emphasize
differences in laboratory and field research or introduce a contributor to a
scientific theory
QUESTION 26
Choice C is the best answer Te author explains that Dialrsquos ldquoaha momentrdquo
came when he determined the Chukars used ldquotheir legs and wings coop-erativelyrdquo to scale the hay bales (lines 40-42) Dial then created additional
experiments to study how the birds dealt with gradually steeper inclines
ldquo[he filmed] the birds as they raced up textured ramps tilted at increasing
anglesrdquo (lines 46-48)
Choices A B and D are incorrect because Dialrsquos ldquoaha momentrdquo was not ol-
lowed by Dial teaching the birds to fly studying videos to find out why the
birds no longer hopped or consulting with other researchers
QUESTION 27
Choice B is the best answer Dial observed that as the Chukars raced up
steep ramps they ldquobegan to flaprdquo and ldquoaimed their flapping down and back-
ward using the orce to keep their eet firmly pressed against the ramprdquo
(lines 49-53) Dial determined that the position o their flapping wings acil-
itated the baby Chukarsrsquo traction on the steep ramps
Choices A C and D are incorrect because the passage does not indicate that
the Chukarsrsquo speed alternation o wing and oot movement or continual
hopping motions acilitated their traction on steep ramps
QUESTION 28
Choice B is the best answer In lines 61-63 the author explains that Dial
named his scientific finding ldquoWAIR or wing-assisted incline running and
went on to document it in a wide range o speciesrdquo In this context Dial
ldquodocumentedrdquo or recorded the existence o WAIR in numerous bird species
Choices A C and D are incorrect because in this context ldquodocumentrdquo does
not mean to portray publish or process
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8
QUESTION 29
Choice D is the best answer In lines 70-74 the author explains that glid-
ing animals do not use a ldquoflapping flight strokerdquo or WAIR wing-assisted
incline running Since Chukars a ground bird use WAIR to help scale steep
inclines it can be reasonably inerred that gliding animals do not use WAIR
to aid in climbing slopes
Choices A B and C are incorrect because the passage does not include
inormation on gliding animalsrsquo offspring their method o locomotion or
their eeding habits
QUESTION 30
Choice D is the best answer In lines 73-75 the author provides evidence
that ldquothe flapping flight strokerdquo is ldquosomething gliding animals donrsquot dordquo
Choices A B and C do not provide the best evidence that gliding animalsdo not use a flapping stroke to aid in climbing slopes Tese choices do not
contain inormation about gliding animals
QUESTION 31
Choice B is the best answer In lines 21-24 the authors o Passage 1 state
societyrsquos ldquocommon happinessrdquo is dependent on women never becoming
involved in politics In this context the authors o Passage 1 are sug-
gesting that all members o society can have a ldquocommonrdquo or shared
happiness
Choices A C and D are incorrect because in this context ldquocommonrdquo does
not mean average coarse or similar
QUESTION 32
Choice C is the best answer In lines 25-30 the authors o Passage 1 state
that women should seek ldquogentle occupations and the cares o the homerdquo
so they can avoid perorming difficult or ldquostrenuousrdquo and unpleasant or
ldquoonerousrdquo tasks
Choices A B and D are incorrect because the authors o Passage 1 do notsuggest that running a household and raising children are rewarding or
both sexes yield less value or society or require proessional or political
skills
QUESTION 33
Choice C is the best answer In lines 25-30 the authors o Passage 1 provide
evidence that women should run households and raise children because
these roles do not require ldquostrenuous habits and onerous dutiesrdquo
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9
Choices A B and D do not provide the best evidence that running a house-
hold and raising children entail very ew activities that are difficult or
unpleasant rather these lines offer general inormation about the differ-
ences between the sexes
QUESTION 34
Choice D is the best answer In lines 41-46 Wollstonecraf argues that i
women do not receive an education ldquoto become the companion o manrdquo or
one that is comparable to menrsquos education then society will not progress in
ldquoknowledge and virtuerdquo
Choices A B and C are incorrect because Wollstonecraf does not suggest
that society can progress only i women have happiness and financial secu-
rity ollow societal rules or replace men as figures o power
QUESTION 35
Choice C is the best answer Wollstonecraf argues that women should be
granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo
(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-
enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context
Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or
intellect and allow women to consider their role in society
Choices A B and D are incorrect because in this context ldquoreasonrdquo does not
mean motive sanity or explanation
QUESTION 36
Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws
passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to
ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf
is arguing that societyrsquos leaders grant men reedoms that are denied to women
Choices B C and D are incorrect because Wollstonecraf does not claim
that societyrsquos leaders have granted reedoms that created a general reduction
in individual virtue caused arguments about happiness or ensured equality
or all people
QUESTION 37
Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-
dence that societyrsquos leaders grant reedoms that privilege men She argues
that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-
lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to
ldquocontend or their reedomrdquo
Choices A B and C do not provide the best evidence that societyrsquos leaders
grant reedoms that privilege men over women
7262019 PrepScholar Sat Practice Test 3 Answers
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10
QUESTION 38
Choice C is the best answer Wollstonecraf cites the statement made by
the authors o Passage 1 that excluding women rom political participation
is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)
Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe
abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument
by highlighting a flaw in the reasoning presented by the authors o Passage 1
Choices A B and D are incorrect because Wollstonecraf does not reer to
the statement made in Passage 1 to call into question the authorsrsquo qualifica-
tions dispute the assertion that women are excluded by their own govern-
ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on
gender roles
QUESTION 39
Choice A is the best answer Te authors o Passage 1 argue that while
restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)
this restriction is necessary or societyrsquos overall happiness (lines 13-17)
Wollstonecraf however strongly challenges this argument asking the
authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-
doms are granted to women and likening societyrsquos male leaders to tyrants as
they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in
the darkrdquo (lines 78-88)
Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2
QUESTION 40
Choice D is the best answer Te authors o Passage 1 admit that women are
ldquoexcluded by the other hal [men] rom any participation in governmentrdquo
(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws
that deny women ldquocivil and political rightsrdquo (line 86)
Choices A B and C are incorrect because the authors o both passages
would not agree that women had the same preerences as men required agood education or were as happy as men
QUESTION 41
Choice A is the best answer Wollstonecraf argues in the final paragraph
o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women
ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would
most likely argue that allowing women these rights would be ldquoa reversal o
[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos
interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as
7262019 PrepScholar Sat Practice Test 3 Answers
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11
mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created
two sexes or a particular reason so while men can exercise civil and politi-
cal rights women are not naturally suited to these activities (lines 30-36)
Choices B and C are incorrect because they are not supported by inorma-
tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do
not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo
QUESTION 42
Choice C is the best answer When discussing problems with bee colo-
nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo
(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-
tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a
tentative tone and provides urther evidence that the authors believe but are
not certain that their hypothesis is correct
Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone
QUESTION 43
Choice C is the best answer In lines 24-28 the authors hypothesize that bee
colonies will be susceptible to mite inestations i they do not occasionally
eed on pyrethrum producing plants In lines 42-46 they suggest creating a
trial where a ldquosmall number o commercial honey bee colonies are offered a
number o pyrethrum producing plantsrdquo to test their hypothesis
Choices A B and D are incorrect because the authors do not hypothesize that
honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees
to develop secondary inections that beekeepers should increase their use o
insecticides or that humans are more susceptible to varroa mites
QUESTION 44
Choice D is the best answer In lines 24-28 the authors provide evidence
that a bee colony may be more resistant to mite inections i the bees eat
pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-
nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees
Choices A B and C do not describe any o the authorsrsquo hypotheses
QUESTION 45
Choice D is the best answer Te authors explain that when beekeepers
use commercially produced insecticides to fight mite inections they may
ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-
cientrdquo (lines 31-35)
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12
Choices A B and C are incorrect because the authors do not suggest that
beekeepersrsquo use o commercially produced insecticides increases mite popu-
lations kills bacteria or destroys beesrsquo primary ood source
QUESTION 46
Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-
ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo
Choices A B and D are incorrect because they do not provide the best evi-
dence that beekeepersrsquo use o commercially produced insecticides may be
harmul to bees choices A B and D ocus on mite inestationsrsquo impact on
honeybees
QUESTION 47
Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some
bees Te authors then state ldquoWe urther postulate that the proper dosage
necessary to prevent mite inestation may be better lef to the beesrdquo (lines
35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the
bees may naturally control mite inestations better than insecticides
Choices A C and D are incorrect because in this context ldquopostulaterdquo does
not mean to make an unounded assumption question a belie or theory or
conclude based on firm evidence
QUESTION 48
Choice B is the best answer In the ourth paragraph the authors propose
a trial to study i honeybeesrsquo consumption o pyrethrum producing plants
helps the honeybees deend against mite inestations In the experiment the
authors plan to offer honey bee colonies both pyrethrum producing plants
and ldquoa typical bee ood source such as cloverrdquo to determine i these different
diets affect the beesrsquo susceptibility to mite inestations
Choices A C and D are incorrect because the main purpose o the ourth
paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished
experiment
QUESTION 49
Choice A is the best answer In lines 43-45 the authors propose a scien-
tific trial in which honeybees are ldquooffered a number o pyrethrum producing
plants as well as a typical bee ood source such as cloverrdquo Since the authors
contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood
sourcerdquo it can be assumed that clover does not produce pyrethrums
7262019 PrepScholar Sat Practice Test 3 Answers
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13
Choice B is incorrect because it is stated in the passage Choices C and D are
incorrect because they are not assumptions made by the authors
QUESTION 50
Choice B is the best answer Te table shows that 77 percent o the honeybee
colonies with colony collapse disorder were inected by all our pathogens
Choices A C and D are incorrect because they do not identiy the percent
o honeybee colonies with colony collapse disorder that were inected by all
our pathogens as based on data in the table
QUESTION 51
Choice D is the best answer Te table shows that 81 percent o colo-
nies without colony collapse disorder were affected by the pathogen
Nosema ceranae
Choices A B and C are incorrect because they do not identiy the pathogen
that inected the highest percentage o honeybee colonies without colony
collapse disorder as based on data in the table
QUESTION 52
Choice D is the best answer Te table discusses pathogen occurrence in
honeybee colonies but it includes no inormation as to whether these hon-
eybees were inected with mites Because the table does not suggest mites
inested the honeybee colonies no conclusions can be made as to whether
mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)
Choices A B and C are incorrect because the table provides no inormation
about whether these honeybees were inected with mites
Section 2 Writing and Language Test
QUESTION 1
Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-
ates a parallel structure within the list that begins with ldquohappierrdquo
Choices B C and D are incorrect because none creates a parallel structure
within the list o qualities
QUESTION 2
Choice B is the best answer Te ways in which exposure to natural light
affects employees is the main subject o the passage
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1540
14
Choices A C and D are incorrect because none introduces the topic dis-
cussed in the remainder o the passage
QUESTION 3
Choice C is the best answer It accurately notes that the proposed sentence
would be placed directly between the first mention o circadian rhythms andthe explanation o the term
Choices A B and D are incorrect because each misinterprets the relation-
ship between the proposed additional text and the ideas in the paragraph
QUESTION 4
Choice C is the best answer It provides the correct possessive construction
or ldquobodyrdquo which must be a singular noun when discussed in general terms
as in this sentence Choice C also provides the correct plural construction
or ldquoclocksrdquo
Choices A B and D are incorrect because each applies either a possessive or
a plural construction in a place where it doesnrsquot belong
QUESTION 5
Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular
noun ldquoabsenteeismrdquo
Choices B C and D are incorrect because each provides a verb that
either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy
QUESTION 6
Choice B is the best answer It contains a direct reerence to productivity
the topic introduced in the previous sentence
Choices A C and D are incorrect because none directly addresses employee
productivity the primary subject o the previous sentence
QUESTION 7
Choice A is the best answer It opens with a reerence to lowered worker
productivity creating a transition rom the previous paragraph and clearly
positions the high energy costs o artificial light sources as an additional
disadvantage
Choices B C and D are incorrect because none o the choices offer an ade-
quate transition rom the previous paragraph Each awkwardly inserts the
issue o lower worker productivity into a statement about the high energy
costs o artificial light sources
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1640
15
QUESTION 8
Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-
cate that the savings occurred every year
Choices A B and C are incorrect because each proposes an option that
would result in a redundancy with ldquoannualrdquo
QUESTION 9
Choice C is the best answer It provides a transitional adverb that accurately
communicates that this sentence describes an option that companies could
choose (ldquolight tubesrdquo) instead o the option described in the previous sen-
tence (ldquoull-pane windowsrdquo)
Choices A B and D are incorrect because each proposes a transitional
adverb that does not accurately reflect the relationship between this sen-
tence and the one preceding it
QUESTION 10
Choice C is the best answer It provides the correct relative pronoun to cor-
respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-
duce the definition that ollows
Choices A B and D are incorrect because each offers a pronoun inappropri-
ate or opening a dependent clause defining ldquolight tubesrdquo
QUESTION 11
Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the
noun ldquomeansrdquo particularly as a way to connect it to another noun or verb
Choices A C and D are incorrect because each results in nonstandard
phrasing with ldquomeansrdquo
QUESTION 12
Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-
responds with the plural noun ldquosettlersrdquo
Choices B C and D are incorrect because each provides either a nonstan-
dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo
QUESTION 13
Choice C is the best answer It creates a transition rom the poor ood qual-
ity mentioned in the previous sentence to the inormation about Harvey in
the remainder o the sentence
7262019 PrepScholar Sat Practice Test 3 Answers
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16
Choices A B and D are incorrect because none offers a transition rom the
previous sentence or a detail that corresponds precisely with the inorma-
tion in the remainder o the sentence
QUESTION 14
Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens
with a comma
Choices A B and C are incorrect because each proposes punctuation that
creates an inappropriately strong separation between the subject ldquoFred
Harveyrdquo and the verb ldquodecidedrdquo
QUESTION 15
Choice B is the best answer It provides the plural verb and plural posses-
sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo
Choices A C and D are incorrect because each either ails to provide a verb
that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide
the appropriate possessive pronoun
QUESTION 16
Choice C is the best answer It accurately echoes an earlier characterization
o the ood as being o ldquoterrible qualityrdquo while maintaining the established
tone o the passage
Choices A B and D are incorrect either because the word is less ormal than
the established tone o the passage (ldquoickyrdquo) or because it illogically attributes
agency to ood (ldquosinisterrdquo ldquosurlyrdquo)
QUESTION 17
Choice C is the best answer It accurately interprets ldquonot content to ollow
conventional business practicesrdquo as logically introducing the new practice o
ldquoemploying womenrdquo described in the ollowing sentences
Choices A B and D are incorrect because none recognizes why the sentence
is relevant to this particular location in the passage
QUESTION 18
Choice B is the best answer It is concise and ree o redundancies
Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and
ldquotremendousrdquo adjectives so close in meaning that together they present a
redundancy
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840
17
QUESTION 19
Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary
reerence to ldquosuch regulationsrdquo in the previous clause
Choices A B and C are incorrect because each lacks a necessary subject
such as a pronoun or noun
QUESTION 20
Choice C is the best answer It reers directly to benefits or the restaurantsrsquo
emale employees the subject o the previous sentence
Choices A B and D are incorrect because none logically builds upon the
sentence that precedes it
QUESTION 21
Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo
Choices A B and C are incorrect because each uses the punctuation or
a dependent clause (ldquoLiving independently and demonstrating an intense
work ethicrdquo) as i it were an independent clause
QUESTION 22
Choice A is the best answer It recognizes that the new inormation sup-
ports the previous sentencersquos claim that ldquothe Harvey Girls became known as
a transormative orcerdquo
Choices B C and D are incorrect because each misinterprets the relation-
ship between the proposed text and the passage
QUESTION 23
Choice A is the best answer It opens with a clause that identifies how
1-MCP affects apples which ocuses the sentence on 1-MCP as the subject
and allows the ideas in the sentence to progress logically
Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy
QUESTION 24
Choice D is the best answer Only the comma is necessary to separate
ldquoethylenerdquo rom the appositive noun phrase that defines it
Choices A B and C are incorrect because each creates a comma splice and
or adds unnecessary words
7262019 PrepScholar Sat Practice Test 3 Answers
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18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040
19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340
22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440
23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640
25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940
28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040
29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040
QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 240
1
Answer Explanations
SAT Practice Test 3
Section 1 Reading Test
QUESTION 1
Choice B is the best answer In the passage Lady Carlotta is approachedby the ldquoimposingly attired ladyrdquo Mrs Quabarl while standing at a train sta-
tion (lines 32-35) Mrs Quabarl assumes Lady Carlotta is her new nanny
Miss Hope ldquoYou must be Miss Hope the governess Irsquove come to meetrdquo (lines
36-37) Lady Carlotta does not correct Mrs Quabarlrsquos mistake and replies
ldquoVery well i I must I mustrdquo (line 39)
Choices A C and D are incorrect because the passage is not about a woman
weighing a job choice seeking revenge on an acquaintance or disliking her
new employer
QUESTION 2
Choice C is the best answer In lines 1-3 the narrator states that Lady
Carlotta ldquostepped out on to the platorm o the small wayside station and
took a turn or two up and down its uninteresting lengthrdquo in order to ldquokill
timerdquo In this context Lady Carlotta was taking a ldquoturnrdquo or a short walk
along the platorm while waiting or the train to leave the station
Choices A B and D are incorrect because in this context ldquoturnrdquo does not
mean slight movement change in rotation or course correction While Lady
Carlotta may have had to rotate her body while moving across the station
ldquotook a turnrdquo implies that Lady Carlotta took a short walk along the plat-
ormrsquos length
QUESTION 3
Choice A is the best answer In lines 10-14 the narrator states that some o
Lady Carlottarsquos acquaintances would ofen admonish or criticize Lady Carlotta
or meddling in or openly expressing her opinion on other peoplersquos affairs
Choices B C and D are incorrect because the narrator does not suggest that
other people viewed Lady Carlotta as tactul ambitious or unriendly
7262019 PrepScholar Sat Practice Test 3 Answers
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2
QUESTION 4
Choice A is the best answer In lines 10-14 the narrator states that people
ofen criticized Lady Carlotta and suggested that she not interere in other
peoplersquos affairs which were ldquonone o her businessrdquo Te act that people
ofen were critical o Lady Carlottarsquos behavior provides evidence that Lady
Carlotta was outspoken
Choices B C and D do not provide the best evidence that Lady Carlotta was
outspoken Choices B C and D mention Lady Carlotta but do not speciy
how others view her
QUESTION 5
Choice C is the best answer Te narrator notes that Lady Carlotta decided
not to interere when one o her ldquomost eloquent exponentsrdquo was stuck in a
tree because an angry boar was nearby (lines 14-22) Tis ldquoeloquent expo-
nentrdquo was a woman who ofen criticized Lady Carlotta or interering inother peoplersquos affairs Lady Carlottarsquos decision to ldquoput the doctrine o non-
intererence into practicerdquo (to not help her emale acquaintance who was
ldquobesiegedrdquo in a tree) suggests that Lady Carlotta has a sense o humor
Choices A B and D are incorrect because the description o how she ldquoput
the doctrine o non-intererence into practicerdquo does not suggest that Lady
Carlotta is deceptive or cruel or explain a surprising change in her behavior
QUESTION 6
Choice A is the best answer Te narrator explains that Mrs Quabarl toldLady Carlotta about the ldquonature o the chargerdquo when she gave Lady Carlotta
details about the Quabarl children (line 53-61) Since Lady Carlotta is pre-
tending to be a governess the term ldquochargerdquo reers to her responsibilities or
job duties when caring or the Quabarl children
Choices B C and D are incorrect because in this context ldquochargerdquo does not
mean attack ee or expense
QUESTION 7
Choice A is the best answer Lady Carlotta learns about Mrs Quabarlrsquos chil-dren Claude Wilrid and Irene (lines 53-58) Te narrator then describes
Mrs Quabarlrsquos child Viola as ldquosomething or other else o a mould equally
commonplace among children o that class and type in the twentieth cen-
turyrdquo (lines 58-61) Tis statement about Viola implies that all o the Quabarl
children have skills typical or ldquoo a mould equally commonplacerdquo to other
peers in their social class
Choices B C and D are incorrect because the narrator does not indicate that
all o the Quabarl children are unusually creative and intelligent hostile to
the idea o having a governess or more educated than their peers
7262019 PrepScholar Sat Practice Test 3 Answers
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3
QUESTION 8
Choice B is the best answer In lines 62-69 Mrs Quabarl explains to Lady
Carlotta that she wants her children to actively participate in their education
and that Lady Carlotta should not create lessons that require her children to
simply memorize historical figures and dates Mrs Quabarl emphasizes an
education centered on active engagement when she states that her childrenshould ldquonot only be AUGH but INERESED in what they learnrdquo
Choices A C and D are incorrect because the narrator does not suggest that
Mrs Quabarl avors an education that emphasizes traditional values artistic
experimentation or actual retention
QUESTION 9
Choice B is the best answer In lines 77-82 the narrator describes Mrs
Quabarl as appearing ldquomagnificent and autocraticrdquo or outwardly domineer-
ing but easily ldquocowed and apologeticrdquo when someone challenges or defiesher authority
Choices A C and D are incorrect because the narrator does not describe
Mrs Quabarl as selfish bitter or requently imprudent
QUESTION 10
Choice D is the best answer In lines 77-82 the narrator provides evidence
that Mrs Quabarl appears imposing or autocratic but is easily defied or
opposed ldquoShe was one o those imperectly sel-assured individuals who are
magnificent and autocratic as long as they are not seriously opposed Teleast show o unexpected resistance goes a long way towards rendering them
cowed and apologeticrdquo
Choices A B and C do not provide the best evidence that Mrs Quabarl
appears imposing but is easily defied Choices A and B are incorrect because
they present Mrs Quabarlrsquos opinions on railway companies and educa-
tion and choice C is incorrect because it ocuses on Lady Carlotta not
Mrs Quabarl
QUESTION 11
Choice A is the best answer While the author predominantly supports
the use o public transportation in the third paragraph he recognizes
some limitations to the public transportation system it is a ldquodepressing
experiencerdquo (lines 25-26) and ldquounderunded ill-maintained and
ill-plannedrdquo (line 31)
Choices B C and D are incorrect because the third paragraph does not
expand upon an argument made in the first two paragraphs provide an
overview o a problem or advocate ending the use o public transportation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 540
4
QUESTION 12
Choice C is the best answer Te author notes that in North America ldquohopping
in a car almost always gets you to your destination more quicklyrdquo (lines 32-34)
Tis statement suggests that speed is one advantage to driving in North America
Choices A B and D are incorrect because the author does not cite environmen-
tal impact convenience or cost as advantages o driving in North America
QUESTION 13
Choice D is the best answer In lines 32-34 the author provides evidence
that speed is one advantage to driving in North America because driving
ldquoalmost always gets you to your destination more quicklyrdquo
Choices A B and C do not provide the best evidence that speed is one
advantage to driving in North America Choices A and B are incorrect
because they offer general inormation about using public transportationChoice C is incorrect because although these lines mention North America
they ocus on the disadvantages o public transportation
QUESTION 14
Choice B is the best answer Te author argues in the ourth paragraph that
public transportation ldquocan be aster more comortable and cheaper than the
private automobilerdquo (lines 36-37) and provides examples o ast and conve-
nient public transportation systems
Choices A C and D are incorrect because they ocus on points made in theourth paragraph rather than the paragraphrsquos central idea
QUESTION 15
Choice B is the best answer In lines 35-37 the author provides evidence
that some public transportation systems are superior to driving because
public transportation ldquocan be aster more comortable and cheaper than the
private automobilerdquo
Choices A C and D do not provide the best evidence that some public
transportation systems are superior to driving as they highlight points madein the ourth paragraph rather than the paragraphrsquos central idea
QUESTION 16
Choice C is the best answer In the last paragraph the author explains the
trend that people who became adults around the end o the twentieth cen-
tury are more willing to use public transportation than people rom older
generations Te author notes ldquoI you credit the demographers this transit
trend has legsrdquo (lines 58-59) In this context ldquocreditrdquo means to believe the
demographersrsquo claims about the trend
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 640
5
Choices A B and D are incorrect because in this context ldquocreditrdquo does not
mean endow attribute or honor
QUESTION 17
Choice B is the best answer In lines 59-63 the author explains the trend
o people who became adults around the end o the twentieth centuryldquotend[ing] to avor cities over suburbsrdquo In this context these adults ldquoavorrdquo
or preer cities over suburbs
Choices A C and D are incorrect because in this context ldquoavorrdquo does not
mean indulge resemble or serve
QUESTION 18
Choice B is the best answer In lines 63-67 the author explains that while
riding on public transportation people can use personal electronic devices
such as ldquoiPads MP3 players Kindles and smartphonesrdquo
Choices A C and D are incorrect because they do not show that public
transportation is compatible with the use o personal electronic devices
QUESTION 19
Choice A is the best answer Figure 1 shows that 107 o public transpor-
tation passengers are students and 67 o public transportation passengers
are retirees Tus more students than retirees use public transportation
Choices B and C are incorrect because figure 1 shows that more employedthan unemployed people use public transportation and that more employed
people than homemakers use public transportation Choice D is incorrect
because figure 1 does not explain how requently passengers use public
transportation it only identifies public transportation passengers by their
primary occupation
QUESTION 20
Choice A is the best answer Figure 1 shows that 72 o public transporta-
tion passengers are ldquoemployed outside the homerdquo and figure 2 indicates that
591 o public transportation trips are or ldquoworkrdquo It can be inerred romthese figures that many public transportation passengers take public trans-
portation to their place o employment
Choices B C and D are incorrect because figure 1 and figure 2 do not
indicate that public transportation passengers primarily use the system to
run errands use their own car on weekends or are planning to purchase
a car
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 740
6
QUESTION 21
Choice D is the best answer Te author explains that Ken Dial created an
experiment to study the evolution o flight by observing how baby Chukars
learn to fly During the experiment Dial noticed the unusual way Chukars
use their ldquolsquowings and legs cooperativelyrsquordquo to scale hay bales (lines 38-43) and
he created ldquoa series o ingenious experimentsrdquo (line 46) to study this obser- vation Afer his additional experiments Dial determined that these baby
birds angle ldquotheir wings differently rom birds in flightrdquo (lines 49-50)
Choices A B and C are incorrect because they do not accurately reflect the
sequence o events in the passage
QUESTION 22
Choice A is the best answer In lines 6-9 the author explains that Dial was
ldquochallengedrdquo or dared by graduate students to develop ldquonew datardquo on a long-
standing scientific debate (the ldquoground-up-tree-downrdquo theory)
Choices B C and D are incorrect because in this context ldquochallengedrdquo does
not mean required disputed with or competed with
QUESTION 23
Choice A is the best answer Te author explains that Dial created his initial
experiment to try and create ldquonew data on the age-old ground-up-tree-down
debaterdquo and that he looked or ldquocluesrdquo in ldquohow baby game birds learned to
flyrdquo (lines 8-11) Te note at the beginning o the passage explains the ldquoage-
old ground-up-tree down debaterdquo and offers two different theories on howbirds evolved to fly Finally the last paragraph o the passage discusses WAIR
in an evolutionary context
Choices B C and D are incorrect because they do not identiy Dialrsquos central
assumption in setting up his research
QUESTION 24
Choice B is the best answer In lines 6-11 the author provides evidence that
Dialrsquos central assumption in setting up his research is that the acquisition o
flight in young birds is linked to the acquisition o flight in their ancestorsTe author notes that Dial created a project to ldquocome up with new data on
the age-old ground-up-tree-down debaterdquo
Choices A C and D do not provide the best evidence that Dialrsquos central
assumption in setting up his research is that the acquisition o flight in young
birds is linked to the acquisition o flight in their ancestors Choices A C
and D are incorrect because they ocus on Dialrsquos experiment and his obser-
vations on ground birds
7262019 PrepScholar Sat Practice Test 3 Answers
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7
QUESTION 25
Choice C is the best answer When a rancher observed Dialrsquos laboratory
setup he was ldquoincredulousrdquo that the Chukars were living on the ground and
he advised Dial to give the birds ldquosomething to climb onrdquo (lines 16-23) Tis
ldquokey piece o advicerdquo (line 14) led Dial to add hay bales to his laboratory
Dial later noticed that the Chukars were using their legs and wings to scalethe hay bales and this observation became the ocal point o his research
Choices A B and D are incorrect because the incident with the local rancher
did not serve to reveal Dialrsquos motivation or creating the project emphasize
differences in laboratory and field research or introduce a contributor to a
scientific theory
QUESTION 26
Choice C is the best answer Te author explains that Dialrsquos ldquoaha momentrdquo
came when he determined the Chukars used ldquotheir legs and wings coop-erativelyrdquo to scale the hay bales (lines 40-42) Dial then created additional
experiments to study how the birds dealt with gradually steeper inclines
ldquo[he filmed] the birds as they raced up textured ramps tilted at increasing
anglesrdquo (lines 46-48)
Choices A B and D are incorrect because Dialrsquos ldquoaha momentrdquo was not ol-
lowed by Dial teaching the birds to fly studying videos to find out why the
birds no longer hopped or consulting with other researchers
QUESTION 27
Choice B is the best answer Dial observed that as the Chukars raced up
steep ramps they ldquobegan to flaprdquo and ldquoaimed their flapping down and back-
ward using the orce to keep their eet firmly pressed against the ramprdquo
(lines 49-53) Dial determined that the position o their flapping wings acil-
itated the baby Chukarsrsquo traction on the steep ramps
Choices A C and D are incorrect because the passage does not indicate that
the Chukarsrsquo speed alternation o wing and oot movement or continual
hopping motions acilitated their traction on steep ramps
QUESTION 28
Choice B is the best answer In lines 61-63 the author explains that Dial
named his scientific finding ldquoWAIR or wing-assisted incline running and
went on to document it in a wide range o speciesrdquo In this context Dial
ldquodocumentedrdquo or recorded the existence o WAIR in numerous bird species
Choices A C and D are incorrect because in this context ldquodocumentrdquo does
not mean to portray publish or process
7262019 PrepScholar Sat Practice Test 3 Answers
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8
QUESTION 29
Choice D is the best answer In lines 70-74 the author explains that glid-
ing animals do not use a ldquoflapping flight strokerdquo or WAIR wing-assisted
incline running Since Chukars a ground bird use WAIR to help scale steep
inclines it can be reasonably inerred that gliding animals do not use WAIR
to aid in climbing slopes
Choices A B and C are incorrect because the passage does not include
inormation on gliding animalsrsquo offspring their method o locomotion or
their eeding habits
QUESTION 30
Choice D is the best answer In lines 73-75 the author provides evidence
that ldquothe flapping flight strokerdquo is ldquosomething gliding animals donrsquot dordquo
Choices A B and C do not provide the best evidence that gliding animalsdo not use a flapping stroke to aid in climbing slopes Tese choices do not
contain inormation about gliding animals
QUESTION 31
Choice B is the best answer In lines 21-24 the authors o Passage 1 state
societyrsquos ldquocommon happinessrdquo is dependent on women never becoming
involved in politics In this context the authors o Passage 1 are sug-
gesting that all members o society can have a ldquocommonrdquo or shared
happiness
Choices A C and D are incorrect because in this context ldquocommonrdquo does
not mean average coarse or similar
QUESTION 32
Choice C is the best answer In lines 25-30 the authors o Passage 1 state
that women should seek ldquogentle occupations and the cares o the homerdquo
so they can avoid perorming difficult or ldquostrenuousrdquo and unpleasant or
ldquoonerousrdquo tasks
Choices A B and D are incorrect because the authors o Passage 1 do notsuggest that running a household and raising children are rewarding or
both sexes yield less value or society or require proessional or political
skills
QUESTION 33
Choice C is the best answer In lines 25-30 the authors o Passage 1 provide
evidence that women should run households and raise children because
these roles do not require ldquostrenuous habits and onerous dutiesrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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9
Choices A B and D do not provide the best evidence that running a house-
hold and raising children entail very ew activities that are difficult or
unpleasant rather these lines offer general inormation about the differ-
ences between the sexes
QUESTION 34
Choice D is the best answer In lines 41-46 Wollstonecraf argues that i
women do not receive an education ldquoto become the companion o manrdquo or
one that is comparable to menrsquos education then society will not progress in
ldquoknowledge and virtuerdquo
Choices A B and C are incorrect because Wollstonecraf does not suggest
that society can progress only i women have happiness and financial secu-
rity ollow societal rules or replace men as figures o power
QUESTION 35
Choice C is the best answer Wollstonecraf argues that women should be
granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo
(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-
enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context
Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or
intellect and allow women to consider their role in society
Choices A B and D are incorrect because in this context ldquoreasonrdquo does not
mean motive sanity or explanation
QUESTION 36
Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws
passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to
ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf
is arguing that societyrsquos leaders grant men reedoms that are denied to women
Choices B C and D are incorrect because Wollstonecraf does not claim
that societyrsquos leaders have granted reedoms that created a general reduction
in individual virtue caused arguments about happiness or ensured equality
or all people
QUESTION 37
Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-
dence that societyrsquos leaders grant reedoms that privilege men She argues
that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-
lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to
ldquocontend or their reedomrdquo
Choices A B and C do not provide the best evidence that societyrsquos leaders
grant reedoms that privilege men over women
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1140
10
QUESTION 38
Choice C is the best answer Wollstonecraf cites the statement made by
the authors o Passage 1 that excluding women rom political participation
is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)
Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe
abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument
by highlighting a flaw in the reasoning presented by the authors o Passage 1
Choices A B and D are incorrect because Wollstonecraf does not reer to
the statement made in Passage 1 to call into question the authorsrsquo qualifica-
tions dispute the assertion that women are excluded by their own govern-
ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on
gender roles
QUESTION 39
Choice A is the best answer Te authors o Passage 1 argue that while
restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)
this restriction is necessary or societyrsquos overall happiness (lines 13-17)
Wollstonecraf however strongly challenges this argument asking the
authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-
doms are granted to women and likening societyrsquos male leaders to tyrants as
they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in
the darkrdquo (lines 78-88)
Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2
QUESTION 40
Choice D is the best answer Te authors o Passage 1 admit that women are
ldquoexcluded by the other hal [men] rom any participation in governmentrdquo
(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws
that deny women ldquocivil and political rightsrdquo (line 86)
Choices A B and C are incorrect because the authors o both passages
would not agree that women had the same preerences as men required agood education or were as happy as men
QUESTION 41
Choice A is the best answer Wollstonecraf argues in the final paragraph
o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women
ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would
most likely argue that allowing women these rights would be ldquoa reversal o
[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos
interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1240
11
mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created
two sexes or a particular reason so while men can exercise civil and politi-
cal rights women are not naturally suited to these activities (lines 30-36)
Choices B and C are incorrect because they are not supported by inorma-
tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do
not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo
QUESTION 42
Choice C is the best answer When discussing problems with bee colo-
nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo
(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-
tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a
tentative tone and provides urther evidence that the authors believe but are
not certain that their hypothesis is correct
Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone
QUESTION 43
Choice C is the best answer In lines 24-28 the authors hypothesize that bee
colonies will be susceptible to mite inestations i they do not occasionally
eed on pyrethrum producing plants In lines 42-46 they suggest creating a
trial where a ldquosmall number o commercial honey bee colonies are offered a
number o pyrethrum producing plantsrdquo to test their hypothesis
Choices A B and D are incorrect because the authors do not hypothesize that
honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees
to develop secondary inections that beekeepers should increase their use o
insecticides or that humans are more susceptible to varroa mites
QUESTION 44
Choice D is the best answer In lines 24-28 the authors provide evidence
that a bee colony may be more resistant to mite inections i the bees eat
pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-
nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees
Choices A B and C do not describe any o the authorsrsquo hypotheses
QUESTION 45
Choice D is the best answer Te authors explain that when beekeepers
use commercially produced insecticides to fight mite inections they may
ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-
cientrdquo (lines 31-35)
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1340
12
Choices A B and C are incorrect because the authors do not suggest that
beekeepersrsquo use o commercially produced insecticides increases mite popu-
lations kills bacteria or destroys beesrsquo primary ood source
QUESTION 46
Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-
ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo
Choices A B and D are incorrect because they do not provide the best evi-
dence that beekeepersrsquo use o commercially produced insecticides may be
harmul to bees choices A B and D ocus on mite inestationsrsquo impact on
honeybees
QUESTION 47
Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some
bees Te authors then state ldquoWe urther postulate that the proper dosage
necessary to prevent mite inestation may be better lef to the beesrdquo (lines
35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the
bees may naturally control mite inestations better than insecticides
Choices A C and D are incorrect because in this context ldquopostulaterdquo does
not mean to make an unounded assumption question a belie or theory or
conclude based on firm evidence
QUESTION 48
Choice B is the best answer In the ourth paragraph the authors propose
a trial to study i honeybeesrsquo consumption o pyrethrum producing plants
helps the honeybees deend against mite inestations In the experiment the
authors plan to offer honey bee colonies both pyrethrum producing plants
and ldquoa typical bee ood source such as cloverrdquo to determine i these different
diets affect the beesrsquo susceptibility to mite inestations
Choices A C and D are incorrect because the main purpose o the ourth
paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished
experiment
QUESTION 49
Choice A is the best answer In lines 43-45 the authors propose a scien-
tific trial in which honeybees are ldquooffered a number o pyrethrum producing
plants as well as a typical bee ood source such as cloverrdquo Since the authors
contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood
sourcerdquo it can be assumed that clover does not produce pyrethrums
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1440
13
Choice B is incorrect because it is stated in the passage Choices C and D are
incorrect because they are not assumptions made by the authors
QUESTION 50
Choice B is the best answer Te table shows that 77 percent o the honeybee
colonies with colony collapse disorder were inected by all our pathogens
Choices A C and D are incorrect because they do not identiy the percent
o honeybee colonies with colony collapse disorder that were inected by all
our pathogens as based on data in the table
QUESTION 51
Choice D is the best answer Te table shows that 81 percent o colo-
nies without colony collapse disorder were affected by the pathogen
Nosema ceranae
Choices A B and C are incorrect because they do not identiy the pathogen
that inected the highest percentage o honeybee colonies without colony
collapse disorder as based on data in the table
QUESTION 52
Choice D is the best answer Te table discusses pathogen occurrence in
honeybee colonies but it includes no inormation as to whether these hon-
eybees were inected with mites Because the table does not suggest mites
inested the honeybee colonies no conclusions can be made as to whether
mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)
Choices A B and C are incorrect because the table provides no inormation
about whether these honeybees were inected with mites
Section 2 Writing and Language Test
QUESTION 1
Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-
ates a parallel structure within the list that begins with ldquohappierrdquo
Choices B C and D are incorrect because none creates a parallel structure
within the list o qualities
QUESTION 2
Choice B is the best answer Te ways in which exposure to natural light
affects employees is the main subject o the passage
7262019 PrepScholar Sat Practice Test 3 Answers
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14
Choices A C and D are incorrect because none introduces the topic dis-
cussed in the remainder o the passage
QUESTION 3
Choice C is the best answer It accurately notes that the proposed sentence
would be placed directly between the first mention o circadian rhythms andthe explanation o the term
Choices A B and D are incorrect because each misinterprets the relation-
ship between the proposed additional text and the ideas in the paragraph
QUESTION 4
Choice C is the best answer It provides the correct possessive construction
or ldquobodyrdquo which must be a singular noun when discussed in general terms
as in this sentence Choice C also provides the correct plural construction
or ldquoclocksrdquo
Choices A B and D are incorrect because each applies either a possessive or
a plural construction in a place where it doesnrsquot belong
QUESTION 5
Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular
noun ldquoabsenteeismrdquo
Choices B C and D are incorrect because each provides a verb that
either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy
QUESTION 6
Choice B is the best answer It contains a direct reerence to productivity
the topic introduced in the previous sentence
Choices A C and D are incorrect because none directly addresses employee
productivity the primary subject o the previous sentence
QUESTION 7
Choice A is the best answer It opens with a reerence to lowered worker
productivity creating a transition rom the previous paragraph and clearly
positions the high energy costs o artificial light sources as an additional
disadvantage
Choices B C and D are incorrect because none o the choices offer an ade-
quate transition rom the previous paragraph Each awkwardly inserts the
issue o lower worker productivity into a statement about the high energy
costs o artificial light sources
7262019 PrepScholar Sat Practice Test 3 Answers
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15
QUESTION 8
Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-
cate that the savings occurred every year
Choices A B and C are incorrect because each proposes an option that
would result in a redundancy with ldquoannualrdquo
QUESTION 9
Choice C is the best answer It provides a transitional adverb that accurately
communicates that this sentence describes an option that companies could
choose (ldquolight tubesrdquo) instead o the option described in the previous sen-
tence (ldquoull-pane windowsrdquo)
Choices A B and D are incorrect because each proposes a transitional
adverb that does not accurately reflect the relationship between this sen-
tence and the one preceding it
QUESTION 10
Choice C is the best answer It provides the correct relative pronoun to cor-
respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-
duce the definition that ollows
Choices A B and D are incorrect because each offers a pronoun inappropri-
ate or opening a dependent clause defining ldquolight tubesrdquo
QUESTION 11
Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the
noun ldquomeansrdquo particularly as a way to connect it to another noun or verb
Choices A C and D are incorrect because each results in nonstandard
phrasing with ldquomeansrdquo
QUESTION 12
Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-
responds with the plural noun ldquosettlersrdquo
Choices B C and D are incorrect because each provides either a nonstan-
dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo
QUESTION 13
Choice C is the best answer It creates a transition rom the poor ood qual-
ity mentioned in the previous sentence to the inormation about Harvey in
the remainder o the sentence
7262019 PrepScholar Sat Practice Test 3 Answers
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16
Choices A B and D are incorrect because none offers a transition rom the
previous sentence or a detail that corresponds precisely with the inorma-
tion in the remainder o the sentence
QUESTION 14
Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens
with a comma
Choices A B and C are incorrect because each proposes punctuation that
creates an inappropriately strong separation between the subject ldquoFred
Harveyrdquo and the verb ldquodecidedrdquo
QUESTION 15
Choice B is the best answer It provides the plural verb and plural posses-
sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo
Choices A C and D are incorrect because each either ails to provide a verb
that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide
the appropriate possessive pronoun
QUESTION 16
Choice C is the best answer It accurately echoes an earlier characterization
o the ood as being o ldquoterrible qualityrdquo while maintaining the established
tone o the passage
Choices A B and D are incorrect either because the word is less ormal than
the established tone o the passage (ldquoickyrdquo) or because it illogically attributes
agency to ood (ldquosinisterrdquo ldquosurlyrdquo)
QUESTION 17
Choice C is the best answer It accurately interprets ldquonot content to ollow
conventional business practicesrdquo as logically introducing the new practice o
ldquoemploying womenrdquo described in the ollowing sentences
Choices A B and D are incorrect because none recognizes why the sentence
is relevant to this particular location in the passage
QUESTION 18
Choice B is the best answer It is concise and ree o redundancies
Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and
ldquotremendousrdquo adjectives so close in meaning that together they present a
redundancy
7262019 PrepScholar Sat Practice Test 3 Answers
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17
QUESTION 19
Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary
reerence to ldquosuch regulationsrdquo in the previous clause
Choices A B and C are incorrect because each lacks a necessary subject
such as a pronoun or noun
QUESTION 20
Choice C is the best answer It reers directly to benefits or the restaurantsrsquo
emale employees the subject o the previous sentence
Choices A B and D are incorrect because none logically builds upon the
sentence that precedes it
QUESTION 21
Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo
Choices A B and C are incorrect because each uses the punctuation or
a dependent clause (ldquoLiving independently and demonstrating an intense
work ethicrdquo) as i it were an independent clause
QUESTION 22
Choice A is the best answer It recognizes that the new inormation sup-
ports the previous sentencersquos claim that ldquothe Harvey Girls became known as
a transormative orcerdquo
Choices B C and D are incorrect because each misinterprets the relation-
ship between the proposed text and the passage
QUESTION 23
Choice A is the best answer It opens with a clause that identifies how
1-MCP affects apples which ocuses the sentence on 1-MCP as the subject
and allows the ideas in the sentence to progress logically
Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy
QUESTION 24
Choice D is the best answer Only the comma is necessary to separate
ldquoethylenerdquo rom the appositive noun phrase that defines it
Choices A B and C are incorrect because each creates a comma splice and
or adds unnecessary words
7262019 PrepScholar Sat Practice Test 3 Answers
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18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
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19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340
22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640
25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940
28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040
29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3940
38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040
QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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2
QUESTION 4
Choice A is the best answer In lines 10-14 the narrator states that people
ofen criticized Lady Carlotta and suggested that she not interere in other
peoplersquos affairs which were ldquonone o her businessrdquo Te act that people
ofen were critical o Lady Carlottarsquos behavior provides evidence that Lady
Carlotta was outspoken
Choices B C and D do not provide the best evidence that Lady Carlotta was
outspoken Choices B C and D mention Lady Carlotta but do not speciy
how others view her
QUESTION 5
Choice C is the best answer Te narrator notes that Lady Carlotta decided
not to interere when one o her ldquomost eloquent exponentsrdquo was stuck in a
tree because an angry boar was nearby (lines 14-22) Tis ldquoeloquent expo-
nentrdquo was a woman who ofen criticized Lady Carlotta or interering inother peoplersquos affairs Lady Carlottarsquos decision to ldquoput the doctrine o non-
intererence into practicerdquo (to not help her emale acquaintance who was
ldquobesiegedrdquo in a tree) suggests that Lady Carlotta has a sense o humor
Choices A B and D are incorrect because the description o how she ldquoput
the doctrine o non-intererence into practicerdquo does not suggest that Lady
Carlotta is deceptive or cruel or explain a surprising change in her behavior
QUESTION 6
Choice A is the best answer Te narrator explains that Mrs Quabarl toldLady Carlotta about the ldquonature o the chargerdquo when she gave Lady Carlotta
details about the Quabarl children (line 53-61) Since Lady Carlotta is pre-
tending to be a governess the term ldquochargerdquo reers to her responsibilities or
job duties when caring or the Quabarl children
Choices B C and D are incorrect because in this context ldquochargerdquo does not
mean attack ee or expense
QUESTION 7
Choice A is the best answer Lady Carlotta learns about Mrs Quabarlrsquos chil-dren Claude Wilrid and Irene (lines 53-58) Te narrator then describes
Mrs Quabarlrsquos child Viola as ldquosomething or other else o a mould equally
commonplace among children o that class and type in the twentieth cen-
turyrdquo (lines 58-61) Tis statement about Viola implies that all o the Quabarl
children have skills typical or ldquoo a mould equally commonplacerdquo to other
peers in their social class
Choices B C and D are incorrect because the narrator does not indicate that
all o the Quabarl children are unusually creative and intelligent hostile to
the idea o having a governess or more educated than their peers
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 440
3
QUESTION 8
Choice B is the best answer In lines 62-69 Mrs Quabarl explains to Lady
Carlotta that she wants her children to actively participate in their education
and that Lady Carlotta should not create lessons that require her children to
simply memorize historical figures and dates Mrs Quabarl emphasizes an
education centered on active engagement when she states that her childrenshould ldquonot only be AUGH but INERESED in what they learnrdquo
Choices A C and D are incorrect because the narrator does not suggest that
Mrs Quabarl avors an education that emphasizes traditional values artistic
experimentation or actual retention
QUESTION 9
Choice B is the best answer In lines 77-82 the narrator describes Mrs
Quabarl as appearing ldquomagnificent and autocraticrdquo or outwardly domineer-
ing but easily ldquocowed and apologeticrdquo when someone challenges or defiesher authority
Choices A C and D are incorrect because the narrator does not describe
Mrs Quabarl as selfish bitter or requently imprudent
QUESTION 10
Choice D is the best answer In lines 77-82 the narrator provides evidence
that Mrs Quabarl appears imposing or autocratic but is easily defied or
opposed ldquoShe was one o those imperectly sel-assured individuals who are
magnificent and autocratic as long as they are not seriously opposed Teleast show o unexpected resistance goes a long way towards rendering them
cowed and apologeticrdquo
Choices A B and C do not provide the best evidence that Mrs Quabarl
appears imposing but is easily defied Choices A and B are incorrect because
they present Mrs Quabarlrsquos opinions on railway companies and educa-
tion and choice C is incorrect because it ocuses on Lady Carlotta not
Mrs Quabarl
QUESTION 11
Choice A is the best answer While the author predominantly supports
the use o public transportation in the third paragraph he recognizes
some limitations to the public transportation system it is a ldquodepressing
experiencerdquo (lines 25-26) and ldquounderunded ill-maintained and
ill-plannedrdquo (line 31)
Choices B C and D are incorrect because the third paragraph does not
expand upon an argument made in the first two paragraphs provide an
overview o a problem or advocate ending the use o public transportation
7262019 PrepScholar Sat Practice Test 3 Answers
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4
QUESTION 12
Choice C is the best answer Te author notes that in North America ldquohopping
in a car almost always gets you to your destination more quicklyrdquo (lines 32-34)
Tis statement suggests that speed is one advantage to driving in North America
Choices A B and D are incorrect because the author does not cite environmen-
tal impact convenience or cost as advantages o driving in North America
QUESTION 13
Choice D is the best answer In lines 32-34 the author provides evidence
that speed is one advantage to driving in North America because driving
ldquoalmost always gets you to your destination more quicklyrdquo
Choices A B and C do not provide the best evidence that speed is one
advantage to driving in North America Choices A and B are incorrect
because they offer general inormation about using public transportationChoice C is incorrect because although these lines mention North America
they ocus on the disadvantages o public transportation
QUESTION 14
Choice B is the best answer Te author argues in the ourth paragraph that
public transportation ldquocan be aster more comortable and cheaper than the
private automobilerdquo (lines 36-37) and provides examples o ast and conve-
nient public transportation systems
Choices A C and D are incorrect because they ocus on points made in theourth paragraph rather than the paragraphrsquos central idea
QUESTION 15
Choice B is the best answer In lines 35-37 the author provides evidence
that some public transportation systems are superior to driving because
public transportation ldquocan be aster more comortable and cheaper than the
private automobilerdquo
Choices A C and D do not provide the best evidence that some public
transportation systems are superior to driving as they highlight points madein the ourth paragraph rather than the paragraphrsquos central idea
QUESTION 16
Choice C is the best answer In the last paragraph the author explains the
trend that people who became adults around the end o the twentieth cen-
tury are more willing to use public transportation than people rom older
generations Te author notes ldquoI you credit the demographers this transit
trend has legsrdquo (lines 58-59) In this context ldquocreditrdquo means to believe the
demographersrsquo claims about the trend
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 640
5
Choices A B and D are incorrect because in this context ldquocreditrdquo does not
mean endow attribute or honor
QUESTION 17
Choice B is the best answer In lines 59-63 the author explains the trend
o people who became adults around the end o the twentieth centuryldquotend[ing] to avor cities over suburbsrdquo In this context these adults ldquoavorrdquo
or preer cities over suburbs
Choices A C and D are incorrect because in this context ldquoavorrdquo does not
mean indulge resemble or serve
QUESTION 18
Choice B is the best answer In lines 63-67 the author explains that while
riding on public transportation people can use personal electronic devices
such as ldquoiPads MP3 players Kindles and smartphonesrdquo
Choices A C and D are incorrect because they do not show that public
transportation is compatible with the use o personal electronic devices
QUESTION 19
Choice A is the best answer Figure 1 shows that 107 o public transpor-
tation passengers are students and 67 o public transportation passengers
are retirees Tus more students than retirees use public transportation
Choices B and C are incorrect because figure 1 shows that more employedthan unemployed people use public transportation and that more employed
people than homemakers use public transportation Choice D is incorrect
because figure 1 does not explain how requently passengers use public
transportation it only identifies public transportation passengers by their
primary occupation
QUESTION 20
Choice A is the best answer Figure 1 shows that 72 o public transporta-
tion passengers are ldquoemployed outside the homerdquo and figure 2 indicates that
591 o public transportation trips are or ldquoworkrdquo It can be inerred romthese figures that many public transportation passengers take public trans-
portation to their place o employment
Choices B C and D are incorrect because figure 1 and figure 2 do not
indicate that public transportation passengers primarily use the system to
run errands use their own car on weekends or are planning to purchase
a car
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 740
6
QUESTION 21
Choice D is the best answer Te author explains that Ken Dial created an
experiment to study the evolution o flight by observing how baby Chukars
learn to fly During the experiment Dial noticed the unusual way Chukars
use their ldquolsquowings and legs cooperativelyrsquordquo to scale hay bales (lines 38-43) and
he created ldquoa series o ingenious experimentsrdquo (line 46) to study this obser- vation Afer his additional experiments Dial determined that these baby
birds angle ldquotheir wings differently rom birds in flightrdquo (lines 49-50)
Choices A B and C are incorrect because they do not accurately reflect the
sequence o events in the passage
QUESTION 22
Choice A is the best answer In lines 6-9 the author explains that Dial was
ldquochallengedrdquo or dared by graduate students to develop ldquonew datardquo on a long-
standing scientific debate (the ldquoground-up-tree-downrdquo theory)
Choices B C and D are incorrect because in this context ldquochallengedrdquo does
not mean required disputed with or competed with
QUESTION 23
Choice A is the best answer Te author explains that Dial created his initial
experiment to try and create ldquonew data on the age-old ground-up-tree-down
debaterdquo and that he looked or ldquocluesrdquo in ldquohow baby game birds learned to
flyrdquo (lines 8-11) Te note at the beginning o the passage explains the ldquoage-
old ground-up-tree down debaterdquo and offers two different theories on howbirds evolved to fly Finally the last paragraph o the passage discusses WAIR
in an evolutionary context
Choices B C and D are incorrect because they do not identiy Dialrsquos central
assumption in setting up his research
QUESTION 24
Choice B is the best answer In lines 6-11 the author provides evidence that
Dialrsquos central assumption in setting up his research is that the acquisition o
flight in young birds is linked to the acquisition o flight in their ancestorsTe author notes that Dial created a project to ldquocome up with new data on
the age-old ground-up-tree-down debaterdquo
Choices A C and D do not provide the best evidence that Dialrsquos central
assumption in setting up his research is that the acquisition o flight in young
birds is linked to the acquisition o flight in their ancestors Choices A C
and D are incorrect because they ocus on Dialrsquos experiment and his obser-
vations on ground birds
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 840
7
QUESTION 25
Choice C is the best answer When a rancher observed Dialrsquos laboratory
setup he was ldquoincredulousrdquo that the Chukars were living on the ground and
he advised Dial to give the birds ldquosomething to climb onrdquo (lines 16-23) Tis
ldquokey piece o advicerdquo (line 14) led Dial to add hay bales to his laboratory
Dial later noticed that the Chukars were using their legs and wings to scalethe hay bales and this observation became the ocal point o his research
Choices A B and D are incorrect because the incident with the local rancher
did not serve to reveal Dialrsquos motivation or creating the project emphasize
differences in laboratory and field research or introduce a contributor to a
scientific theory
QUESTION 26
Choice C is the best answer Te author explains that Dialrsquos ldquoaha momentrdquo
came when he determined the Chukars used ldquotheir legs and wings coop-erativelyrdquo to scale the hay bales (lines 40-42) Dial then created additional
experiments to study how the birds dealt with gradually steeper inclines
ldquo[he filmed] the birds as they raced up textured ramps tilted at increasing
anglesrdquo (lines 46-48)
Choices A B and D are incorrect because Dialrsquos ldquoaha momentrdquo was not ol-
lowed by Dial teaching the birds to fly studying videos to find out why the
birds no longer hopped or consulting with other researchers
QUESTION 27
Choice B is the best answer Dial observed that as the Chukars raced up
steep ramps they ldquobegan to flaprdquo and ldquoaimed their flapping down and back-
ward using the orce to keep their eet firmly pressed against the ramprdquo
(lines 49-53) Dial determined that the position o their flapping wings acil-
itated the baby Chukarsrsquo traction on the steep ramps
Choices A C and D are incorrect because the passage does not indicate that
the Chukarsrsquo speed alternation o wing and oot movement or continual
hopping motions acilitated their traction on steep ramps
QUESTION 28
Choice B is the best answer In lines 61-63 the author explains that Dial
named his scientific finding ldquoWAIR or wing-assisted incline running and
went on to document it in a wide range o speciesrdquo In this context Dial
ldquodocumentedrdquo or recorded the existence o WAIR in numerous bird species
Choices A C and D are incorrect because in this context ldquodocumentrdquo does
not mean to portray publish or process
7262019 PrepScholar Sat Practice Test 3 Answers
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8
QUESTION 29
Choice D is the best answer In lines 70-74 the author explains that glid-
ing animals do not use a ldquoflapping flight strokerdquo or WAIR wing-assisted
incline running Since Chukars a ground bird use WAIR to help scale steep
inclines it can be reasonably inerred that gliding animals do not use WAIR
to aid in climbing slopes
Choices A B and C are incorrect because the passage does not include
inormation on gliding animalsrsquo offspring their method o locomotion or
their eeding habits
QUESTION 30
Choice D is the best answer In lines 73-75 the author provides evidence
that ldquothe flapping flight strokerdquo is ldquosomething gliding animals donrsquot dordquo
Choices A B and C do not provide the best evidence that gliding animalsdo not use a flapping stroke to aid in climbing slopes Tese choices do not
contain inormation about gliding animals
QUESTION 31
Choice B is the best answer In lines 21-24 the authors o Passage 1 state
societyrsquos ldquocommon happinessrdquo is dependent on women never becoming
involved in politics In this context the authors o Passage 1 are sug-
gesting that all members o society can have a ldquocommonrdquo or shared
happiness
Choices A C and D are incorrect because in this context ldquocommonrdquo does
not mean average coarse or similar
QUESTION 32
Choice C is the best answer In lines 25-30 the authors o Passage 1 state
that women should seek ldquogentle occupations and the cares o the homerdquo
so they can avoid perorming difficult or ldquostrenuousrdquo and unpleasant or
ldquoonerousrdquo tasks
Choices A B and D are incorrect because the authors o Passage 1 do notsuggest that running a household and raising children are rewarding or
both sexes yield less value or society or require proessional or political
skills
QUESTION 33
Choice C is the best answer In lines 25-30 the authors o Passage 1 provide
evidence that women should run households and raise children because
these roles do not require ldquostrenuous habits and onerous dutiesrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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9
Choices A B and D do not provide the best evidence that running a house-
hold and raising children entail very ew activities that are difficult or
unpleasant rather these lines offer general inormation about the differ-
ences between the sexes
QUESTION 34
Choice D is the best answer In lines 41-46 Wollstonecraf argues that i
women do not receive an education ldquoto become the companion o manrdquo or
one that is comparable to menrsquos education then society will not progress in
ldquoknowledge and virtuerdquo
Choices A B and C are incorrect because Wollstonecraf does not suggest
that society can progress only i women have happiness and financial secu-
rity ollow societal rules or replace men as figures o power
QUESTION 35
Choice C is the best answer Wollstonecraf argues that women should be
granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo
(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-
enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context
Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or
intellect and allow women to consider their role in society
Choices A B and D are incorrect because in this context ldquoreasonrdquo does not
mean motive sanity or explanation
QUESTION 36
Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws
passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to
ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf
is arguing that societyrsquos leaders grant men reedoms that are denied to women
Choices B C and D are incorrect because Wollstonecraf does not claim
that societyrsquos leaders have granted reedoms that created a general reduction
in individual virtue caused arguments about happiness or ensured equality
or all people
QUESTION 37
Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-
dence that societyrsquos leaders grant reedoms that privilege men She argues
that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-
lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to
ldquocontend or their reedomrdquo
Choices A B and C do not provide the best evidence that societyrsquos leaders
grant reedoms that privilege men over women
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1140
10
QUESTION 38
Choice C is the best answer Wollstonecraf cites the statement made by
the authors o Passage 1 that excluding women rom political participation
is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)
Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe
abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument
by highlighting a flaw in the reasoning presented by the authors o Passage 1
Choices A B and D are incorrect because Wollstonecraf does not reer to
the statement made in Passage 1 to call into question the authorsrsquo qualifica-
tions dispute the assertion that women are excluded by their own govern-
ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on
gender roles
QUESTION 39
Choice A is the best answer Te authors o Passage 1 argue that while
restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)
this restriction is necessary or societyrsquos overall happiness (lines 13-17)
Wollstonecraf however strongly challenges this argument asking the
authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-
doms are granted to women and likening societyrsquos male leaders to tyrants as
they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in
the darkrdquo (lines 78-88)
Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2
QUESTION 40
Choice D is the best answer Te authors o Passage 1 admit that women are
ldquoexcluded by the other hal [men] rom any participation in governmentrdquo
(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws
that deny women ldquocivil and political rightsrdquo (line 86)
Choices A B and C are incorrect because the authors o both passages
would not agree that women had the same preerences as men required agood education or were as happy as men
QUESTION 41
Choice A is the best answer Wollstonecraf argues in the final paragraph
o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women
ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would
most likely argue that allowing women these rights would be ldquoa reversal o
[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos
interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1240
11
mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created
two sexes or a particular reason so while men can exercise civil and politi-
cal rights women are not naturally suited to these activities (lines 30-36)
Choices B and C are incorrect because they are not supported by inorma-
tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do
not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo
QUESTION 42
Choice C is the best answer When discussing problems with bee colo-
nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo
(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-
tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a
tentative tone and provides urther evidence that the authors believe but are
not certain that their hypothesis is correct
Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone
QUESTION 43
Choice C is the best answer In lines 24-28 the authors hypothesize that bee
colonies will be susceptible to mite inestations i they do not occasionally
eed on pyrethrum producing plants In lines 42-46 they suggest creating a
trial where a ldquosmall number o commercial honey bee colonies are offered a
number o pyrethrum producing plantsrdquo to test their hypothesis
Choices A B and D are incorrect because the authors do not hypothesize that
honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees
to develop secondary inections that beekeepers should increase their use o
insecticides or that humans are more susceptible to varroa mites
QUESTION 44
Choice D is the best answer In lines 24-28 the authors provide evidence
that a bee colony may be more resistant to mite inections i the bees eat
pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-
nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees
Choices A B and C do not describe any o the authorsrsquo hypotheses
QUESTION 45
Choice D is the best answer Te authors explain that when beekeepers
use commercially produced insecticides to fight mite inections they may
ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-
cientrdquo (lines 31-35)
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1340
12
Choices A B and C are incorrect because the authors do not suggest that
beekeepersrsquo use o commercially produced insecticides increases mite popu-
lations kills bacteria or destroys beesrsquo primary ood source
QUESTION 46
Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-
ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo
Choices A B and D are incorrect because they do not provide the best evi-
dence that beekeepersrsquo use o commercially produced insecticides may be
harmul to bees choices A B and D ocus on mite inestationsrsquo impact on
honeybees
QUESTION 47
Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some
bees Te authors then state ldquoWe urther postulate that the proper dosage
necessary to prevent mite inestation may be better lef to the beesrdquo (lines
35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the
bees may naturally control mite inestations better than insecticides
Choices A C and D are incorrect because in this context ldquopostulaterdquo does
not mean to make an unounded assumption question a belie or theory or
conclude based on firm evidence
QUESTION 48
Choice B is the best answer In the ourth paragraph the authors propose
a trial to study i honeybeesrsquo consumption o pyrethrum producing plants
helps the honeybees deend against mite inestations In the experiment the
authors plan to offer honey bee colonies both pyrethrum producing plants
and ldquoa typical bee ood source such as cloverrdquo to determine i these different
diets affect the beesrsquo susceptibility to mite inestations
Choices A C and D are incorrect because the main purpose o the ourth
paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished
experiment
QUESTION 49
Choice A is the best answer In lines 43-45 the authors propose a scien-
tific trial in which honeybees are ldquooffered a number o pyrethrum producing
plants as well as a typical bee ood source such as cloverrdquo Since the authors
contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood
sourcerdquo it can be assumed that clover does not produce pyrethrums
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1440
13
Choice B is incorrect because it is stated in the passage Choices C and D are
incorrect because they are not assumptions made by the authors
QUESTION 50
Choice B is the best answer Te table shows that 77 percent o the honeybee
colonies with colony collapse disorder were inected by all our pathogens
Choices A C and D are incorrect because they do not identiy the percent
o honeybee colonies with colony collapse disorder that were inected by all
our pathogens as based on data in the table
QUESTION 51
Choice D is the best answer Te table shows that 81 percent o colo-
nies without colony collapse disorder were affected by the pathogen
Nosema ceranae
Choices A B and C are incorrect because they do not identiy the pathogen
that inected the highest percentage o honeybee colonies without colony
collapse disorder as based on data in the table
QUESTION 52
Choice D is the best answer Te table discusses pathogen occurrence in
honeybee colonies but it includes no inormation as to whether these hon-
eybees were inected with mites Because the table does not suggest mites
inested the honeybee colonies no conclusions can be made as to whether
mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)
Choices A B and C are incorrect because the table provides no inormation
about whether these honeybees were inected with mites
Section 2 Writing and Language Test
QUESTION 1
Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-
ates a parallel structure within the list that begins with ldquohappierrdquo
Choices B C and D are incorrect because none creates a parallel structure
within the list o qualities
QUESTION 2
Choice B is the best answer Te ways in which exposure to natural light
affects employees is the main subject o the passage
7262019 PrepScholar Sat Practice Test 3 Answers
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14
Choices A C and D are incorrect because none introduces the topic dis-
cussed in the remainder o the passage
QUESTION 3
Choice C is the best answer It accurately notes that the proposed sentence
would be placed directly between the first mention o circadian rhythms andthe explanation o the term
Choices A B and D are incorrect because each misinterprets the relation-
ship between the proposed additional text and the ideas in the paragraph
QUESTION 4
Choice C is the best answer It provides the correct possessive construction
or ldquobodyrdquo which must be a singular noun when discussed in general terms
as in this sentence Choice C also provides the correct plural construction
or ldquoclocksrdquo
Choices A B and D are incorrect because each applies either a possessive or
a plural construction in a place where it doesnrsquot belong
QUESTION 5
Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular
noun ldquoabsenteeismrdquo
Choices B C and D are incorrect because each provides a verb that
either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy
QUESTION 6
Choice B is the best answer It contains a direct reerence to productivity
the topic introduced in the previous sentence
Choices A C and D are incorrect because none directly addresses employee
productivity the primary subject o the previous sentence
QUESTION 7
Choice A is the best answer It opens with a reerence to lowered worker
productivity creating a transition rom the previous paragraph and clearly
positions the high energy costs o artificial light sources as an additional
disadvantage
Choices B C and D are incorrect because none o the choices offer an ade-
quate transition rom the previous paragraph Each awkwardly inserts the
issue o lower worker productivity into a statement about the high energy
costs o artificial light sources
7262019 PrepScholar Sat Practice Test 3 Answers
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15
QUESTION 8
Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-
cate that the savings occurred every year
Choices A B and C are incorrect because each proposes an option that
would result in a redundancy with ldquoannualrdquo
QUESTION 9
Choice C is the best answer It provides a transitional adverb that accurately
communicates that this sentence describes an option that companies could
choose (ldquolight tubesrdquo) instead o the option described in the previous sen-
tence (ldquoull-pane windowsrdquo)
Choices A B and D are incorrect because each proposes a transitional
adverb that does not accurately reflect the relationship between this sen-
tence and the one preceding it
QUESTION 10
Choice C is the best answer It provides the correct relative pronoun to cor-
respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-
duce the definition that ollows
Choices A B and D are incorrect because each offers a pronoun inappropri-
ate or opening a dependent clause defining ldquolight tubesrdquo
QUESTION 11
Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the
noun ldquomeansrdquo particularly as a way to connect it to another noun or verb
Choices A C and D are incorrect because each results in nonstandard
phrasing with ldquomeansrdquo
QUESTION 12
Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-
responds with the plural noun ldquosettlersrdquo
Choices B C and D are incorrect because each provides either a nonstan-
dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo
QUESTION 13
Choice C is the best answer It creates a transition rom the poor ood qual-
ity mentioned in the previous sentence to the inormation about Harvey in
the remainder o the sentence
7262019 PrepScholar Sat Practice Test 3 Answers
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16
Choices A B and D are incorrect because none offers a transition rom the
previous sentence or a detail that corresponds precisely with the inorma-
tion in the remainder o the sentence
QUESTION 14
Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens
with a comma
Choices A B and C are incorrect because each proposes punctuation that
creates an inappropriately strong separation between the subject ldquoFred
Harveyrdquo and the verb ldquodecidedrdquo
QUESTION 15
Choice B is the best answer It provides the plural verb and plural posses-
sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo
Choices A C and D are incorrect because each either ails to provide a verb
that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide
the appropriate possessive pronoun
QUESTION 16
Choice C is the best answer It accurately echoes an earlier characterization
o the ood as being o ldquoterrible qualityrdquo while maintaining the established
tone o the passage
Choices A B and D are incorrect either because the word is less ormal than
the established tone o the passage (ldquoickyrdquo) or because it illogically attributes
agency to ood (ldquosinisterrdquo ldquosurlyrdquo)
QUESTION 17
Choice C is the best answer It accurately interprets ldquonot content to ollow
conventional business practicesrdquo as logically introducing the new practice o
ldquoemploying womenrdquo described in the ollowing sentences
Choices A B and D are incorrect because none recognizes why the sentence
is relevant to this particular location in the passage
QUESTION 18
Choice B is the best answer It is concise and ree o redundancies
Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and
ldquotremendousrdquo adjectives so close in meaning that together they present a
redundancy
7262019 PrepScholar Sat Practice Test 3 Answers
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17
QUESTION 19
Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary
reerence to ldquosuch regulationsrdquo in the previous clause
Choices A B and C are incorrect because each lacks a necessary subject
such as a pronoun or noun
QUESTION 20
Choice C is the best answer It reers directly to benefits or the restaurantsrsquo
emale employees the subject o the previous sentence
Choices A B and D are incorrect because none logically builds upon the
sentence that precedes it
QUESTION 21
Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo
Choices A B and C are incorrect because each uses the punctuation or
a dependent clause (ldquoLiving independently and demonstrating an intense
work ethicrdquo) as i it were an independent clause
QUESTION 22
Choice A is the best answer It recognizes that the new inormation sup-
ports the previous sentencersquos claim that ldquothe Harvey Girls became known as
a transormative orcerdquo
Choices B C and D are incorrect because each misinterprets the relation-
ship between the proposed text and the passage
QUESTION 23
Choice A is the best answer It opens with a clause that identifies how
1-MCP affects apples which ocuses the sentence on 1-MCP as the subject
and allows the ideas in the sentence to progress logically
Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy
QUESTION 24
Choice D is the best answer Only the comma is necessary to separate
ldquoethylenerdquo rom the appositive noun phrase that defines it
Choices A B and C are incorrect because each creates a comma splice and
or adds unnecessary words
7262019 PrepScholar Sat Practice Test 3 Answers
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18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
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19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340
22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640
25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940
28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040
29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3940
38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040
QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 440
3
QUESTION 8
Choice B is the best answer In lines 62-69 Mrs Quabarl explains to Lady
Carlotta that she wants her children to actively participate in their education
and that Lady Carlotta should not create lessons that require her children to
simply memorize historical figures and dates Mrs Quabarl emphasizes an
education centered on active engagement when she states that her childrenshould ldquonot only be AUGH but INERESED in what they learnrdquo
Choices A C and D are incorrect because the narrator does not suggest that
Mrs Quabarl avors an education that emphasizes traditional values artistic
experimentation or actual retention
QUESTION 9
Choice B is the best answer In lines 77-82 the narrator describes Mrs
Quabarl as appearing ldquomagnificent and autocraticrdquo or outwardly domineer-
ing but easily ldquocowed and apologeticrdquo when someone challenges or defiesher authority
Choices A C and D are incorrect because the narrator does not describe
Mrs Quabarl as selfish bitter or requently imprudent
QUESTION 10
Choice D is the best answer In lines 77-82 the narrator provides evidence
that Mrs Quabarl appears imposing or autocratic but is easily defied or
opposed ldquoShe was one o those imperectly sel-assured individuals who are
magnificent and autocratic as long as they are not seriously opposed Teleast show o unexpected resistance goes a long way towards rendering them
cowed and apologeticrdquo
Choices A B and C do not provide the best evidence that Mrs Quabarl
appears imposing but is easily defied Choices A and B are incorrect because
they present Mrs Quabarlrsquos opinions on railway companies and educa-
tion and choice C is incorrect because it ocuses on Lady Carlotta not
Mrs Quabarl
QUESTION 11
Choice A is the best answer While the author predominantly supports
the use o public transportation in the third paragraph he recognizes
some limitations to the public transportation system it is a ldquodepressing
experiencerdquo (lines 25-26) and ldquounderunded ill-maintained and
ill-plannedrdquo (line 31)
Choices B C and D are incorrect because the third paragraph does not
expand upon an argument made in the first two paragraphs provide an
overview o a problem or advocate ending the use o public transportation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 540
4
QUESTION 12
Choice C is the best answer Te author notes that in North America ldquohopping
in a car almost always gets you to your destination more quicklyrdquo (lines 32-34)
Tis statement suggests that speed is one advantage to driving in North America
Choices A B and D are incorrect because the author does not cite environmen-
tal impact convenience or cost as advantages o driving in North America
QUESTION 13
Choice D is the best answer In lines 32-34 the author provides evidence
that speed is one advantage to driving in North America because driving
ldquoalmost always gets you to your destination more quicklyrdquo
Choices A B and C do not provide the best evidence that speed is one
advantage to driving in North America Choices A and B are incorrect
because they offer general inormation about using public transportationChoice C is incorrect because although these lines mention North America
they ocus on the disadvantages o public transportation
QUESTION 14
Choice B is the best answer Te author argues in the ourth paragraph that
public transportation ldquocan be aster more comortable and cheaper than the
private automobilerdquo (lines 36-37) and provides examples o ast and conve-
nient public transportation systems
Choices A C and D are incorrect because they ocus on points made in theourth paragraph rather than the paragraphrsquos central idea
QUESTION 15
Choice B is the best answer In lines 35-37 the author provides evidence
that some public transportation systems are superior to driving because
public transportation ldquocan be aster more comortable and cheaper than the
private automobilerdquo
Choices A C and D do not provide the best evidence that some public
transportation systems are superior to driving as they highlight points madein the ourth paragraph rather than the paragraphrsquos central idea
QUESTION 16
Choice C is the best answer In the last paragraph the author explains the
trend that people who became adults around the end o the twentieth cen-
tury are more willing to use public transportation than people rom older
generations Te author notes ldquoI you credit the demographers this transit
trend has legsrdquo (lines 58-59) In this context ldquocreditrdquo means to believe the
demographersrsquo claims about the trend
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 640
5
Choices A B and D are incorrect because in this context ldquocreditrdquo does not
mean endow attribute or honor
QUESTION 17
Choice B is the best answer In lines 59-63 the author explains the trend
o people who became adults around the end o the twentieth centuryldquotend[ing] to avor cities over suburbsrdquo In this context these adults ldquoavorrdquo
or preer cities over suburbs
Choices A C and D are incorrect because in this context ldquoavorrdquo does not
mean indulge resemble or serve
QUESTION 18
Choice B is the best answer In lines 63-67 the author explains that while
riding on public transportation people can use personal electronic devices
such as ldquoiPads MP3 players Kindles and smartphonesrdquo
Choices A C and D are incorrect because they do not show that public
transportation is compatible with the use o personal electronic devices
QUESTION 19
Choice A is the best answer Figure 1 shows that 107 o public transpor-
tation passengers are students and 67 o public transportation passengers
are retirees Tus more students than retirees use public transportation
Choices B and C are incorrect because figure 1 shows that more employedthan unemployed people use public transportation and that more employed
people than homemakers use public transportation Choice D is incorrect
because figure 1 does not explain how requently passengers use public
transportation it only identifies public transportation passengers by their
primary occupation
QUESTION 20
Choice A is the best answer Figure 1 shows that 72 o public transporta-
tion passengers are ldquoemployed outside the homerdquo and figure 2 indicates that
591 o public transportation trips are or ldquoworkrdquo It can be inerred romthese figures that many public transportation passengers take public trans-
portation to their place o employment
Choices B C and D are incorrect because figure 1 and figure 2 do not
indicate that public transportation passengers primarily use the system to
run errands use their own car on weekends or are planning to purchase
a car
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 740
6
QUESTION 21
Choice D is the best answer Te author explains that Ken Dial created an
experiment to study the evolution o flight by observing how baby Chukars
learn to fly During the experiment Dial noticed the unusual way Chukars
use their ldquolsquowings and legs cooperativelyrsquordquo to scale hay bales (lines 38-43) and
he created ldquoa series o ingenious experimentsrdquo (line 46) to study this obser- vation Afer his additional experiments Dial determined that these baby
birds angle ldquotheir wings differently rom birds in flightrdquo (lines 49-50)
Choices A B and C are incorrect because they do not accurately reflect the
sequence o events in the passage
QUESTION 22
Choice A is the best answer In lines 6-9 the author explains that Dial was
ldquochallengedrdquo or dared by graduate students to develop ldquonew datardquo on a long-
standing scientific debate (the ldquoground-up-tree-downrdquo theory)
Choices B C and D are incorrect because in this context ldquochallengedrdquo does
not mean required disputed with or competed with
QUESTION 23
Choice A is the best answer Te author explains that Dial created his initial
experiment to try and create ldquonew data on the age-old ground-up-tree-down
debaterdquo and that he looked or ldquocluesrdquo in ldquohow baby game birds learned to
flyrdquo (lines 8-11) Te note at the beginning o the passage explains the ldquoage-
old ground-up-tree down debaterdquo and offers two different theories on howbirds evolved to fly Finally the last paragraph o the passage discusses WAIR
in an evolutionary context
Choices B C and D are incorrect because they do not identiy Dialrsquos central
assumption in setting up his research
QUESTION 24
Choice B is the best answer In lines 6-11 the author provides evidence that
Dialrsquos central assumption in setting up his research is that the acquisition o
flight in young birds is linked to the acquisition o flight in their ancestorsTe author notes that Dial created a project to ldquocome up with new data on
the age-old ground-up-tree-down debaterdquo
Choices A C and D do not provide the best evidence that Dialrsquos central
assumption in setting up his research is that the acquisition o flight in young
birds is linked to the acquisition o flight in their ancestors Choices A C
and D are incorrect because they ocus on Dialrsquos experiment and his obser-
vations on ground birds
7262019 PrepScholar Sat Practice Test 3 Answers
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7
QUESTION 25
Choice C is the best answer When a rancher observed Dialrsquos laboratory
setup he was ldquoincredulousrdquo that the Chukars were living on the ground and
he advised Dial to give the birds ldquosomething to climb onrdquo (lines 16-23) Tis
ldquokey piece o advicerdquo (line 14) led Dial to add hay bales to his laboratory
Dial later noticed that the Chukars were using their legs and wings to scalethe hay bales and this observation became the ocal point o his research
Choices A B and D are incorrect because the incident with the local rancher
did not serve to reveal Dialrsquos motivation or creating the project emphasize
differences in laboratory and field research or introduce a contributor to a
scientific theory
QUESTION 26
Choice C is the best answer Te author explains that Dialrsquos ldquoaha momentrdquo
came when he determined the Chukars used ldquotheir legs and wings coop-erativelyrdquo to scale the hay bales (lines 40-42) Dial then created additional
experiments to study how the birds dealt with gradually steeper inclines
ldquo[he filmed] the birds as they raced up textured ramps tilted at increasing
anglesrdquo (lines 46-48)
Choices A B and D are incorrect because Dialrsquos ldquoaha momentrdquo was not ol-
lowed by Dial teaching the birds to fly studying videos to find out why the
birds no longer hopped or consulting with other researchers
QUESTION 27
Choice B is the best answer Dial observed that as the Chukars raced up
steep ramps they ldquobegan to flaprdquo and ldquoaimed their flapping down and back-
ward using the orce to keep their eet firmly pressed against the ramprdquo
(lines 49-53) Dial determined that the position o their flapping wings acil-
itated the baby Chukarsrsquo traction on the steep ramps
Choices A C and D are incorrect because the passage does not indicate that
the Chukarsrsquo speed alternation o wing and oot movement or continual
hopping motions acilitated their traction on steep ramps
QUESTION 28
Choice B is the best answer In lines 61-63 the author explains that Dial
named his scientific finding ldquoWAIR or wing-assisted incline running and
went on to document it in a wide range o speciesrdquo In this context Dial
ldquodocumentedrdquo or recorded the existence o WAIR in numerous bird species
Choices A C and D are incorrect because in this context ldquodocumentrdquo does
not mean to portray publish or process
7262019 PrepScholar Sat Practice Test 3 Answers
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8
QUESTION 29
Choice D is the best answer In lines 70-74 the author explains that glid-
ing animals do not use a ldquoflapping flight strokerdquo or WAIR wing-assisted
incline running Since Chukars a ground bird use WAIR to help scale steep
inclines it can be reasonably inerred that gliding animals do not use WAIR
to aid in climbing slopes
Choices A B and C are incorrect because the passage does not include
inormation on gliding animalsrsquo offspring their method o locomotion or
their eeding habits
QUESTION 30
Choice D is the best answer In lines 73-75 the author provides evidence
that ldquothe flapping flight strokerdquo is ldquosomething gliding animals donrsquot dordquo
Choices A B and C do not provide the best evidence that gliding animalsdo not use a flapping stroke to aid in climbing slopes Tese choices do not
contain inormation about gliding animals
QUESTION 31
Choice B is the best answer In lines 21-24 the authors o Passage 1 state
societyrsquos ldquocommon happinessrdquo is dependent on women never becoming
involved in politics In this context the authors o Passage 1 are sug-
gesting that all members o society can have a ldquocommonrdquo or shared
happiness
Choices A C and D are incorrect because in this context ldquocommonrdquo does
not mean average coarse or similar
QUESTION 32
Choice C is the best answer In lines 25-30 the authors o Passage 1 state
that women should seek ldquogentle occupations and the cares o the homerdquo
so they can avoid perorming difficult or ldquostrenuousrdquo and unpleasant or
ldquoonerousrdquo tasks
Choices A B and D are incorrect because the authors o Passage 1 do notsuggest that running a household and raising children are rewarding or
both sexes yield less value or society or require proessional or political
skills
QUESTION 33
Choice C is the best answer In lines 25-30 the authors o Passage 1 provide
evidence that women should run households and raise children because
these roles do not require ldquostrenuous habits and onerous dutiesrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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9
Choices A B and D do not provide the best evidence that running a house-
hold and raising children entail very ew activities that are difficult or
unpleasant rather these lines offer general inormation about the differ-
ences between the sexes
QUESTION 34
Choice D is the best answer In lines 41-46 Wollstonecraf argues that i
women do not receive an education ldquoto become the companion o manrdquo or
one that is comparable to menrsquos education then society will not progress in
ldquoknowledge and virtuerdquo
Choices A B and C are incorrect because Wollstonecraf does not suggest
that society can progress only i women have happiness and financial secu-
rity ollow societal rules or replace men as figures o power
QUESTION 35
Choice C is the best answer Wollstonecraf argues that women should be
granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo
(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-
enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context
Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or
intellect and allow women to consider their role in society
Choices A B and D are incorrect because in this context ldquoreasonrdquo does not
mean motive sanity or explanation
QUESTION 36
Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws
passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to
ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf
is arguing that societyrsquos leaders grant men reedoms that are denied to women
Choices B C and D are incorrect because Wollstonecraf does not claim
that societyrsquos leaders have granted reedoms that created a general reduction
in individual virtue caused arguments about happiness or ensured equality
or all people
QUESTION 37
Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-
dence that societyrsquos leaders grant reedoms that privilege men She argues
that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-
lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to
ldquocontend or their reedomrdquo
Choices A B and C do not provide the best evidence that societyrsquos leaders
grant reedoms that privilege men over women
7262019 PrepScholar Sat Practice Test 3 Answers
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10
QUESTION 38
Choice C is the best answer Wollstonecraf cites the statement made by
the authors o Passage 1 that excluding women rom political participation
is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)
Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe
abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument
by highlighting a flaw in the reasoning presented by the authors o Passage 1
Choices A B and D are incorrect because Wollstonecraf does not reer to
the statement made in Passage 1 to call into question the authorsrsquo qualifica-
tions dispute the assertion that women are excluded by their own govern-
ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on
gender roles
QUESTION 39
Choice A is the best answer Te authors o Passage 1 argue that while
restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)
this restriction is necessary or societyrsquos overall happiness (lines 13-17)
Wollstonecraf however strongly challenges this argument asking the
authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-
doms are granted to women and likening societyrsquos male leaders to tyrants as
they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in
the darkrdquo (lines 78-88)
Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2
QUESTION 40
Choice D is the best answer Te authors o Passage 1 admit that women are
ldquoexcluded by the other hal [men] rom any participation in governmentrdquo
(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws
that deny women ldquocivil and political rightsrdquo (line 86)
Choices A B and C are incorrect because the authors o both passages
would not agree that women had the same preerences as men required agood education or were as happy as men
QUESTION 41
Choice A is the best answer Wollstonecraf argues in the final paragraph
o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women
ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would
most likely argue that allowing women these rights would be ldquoa reversal o
[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos
interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as
7262019 PrepScholar Sat Practice Test 3 Answers
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11
mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created
two sexes or a particular reason so while men can exercise civil and politi-
cal rights women are not naturally suited to these activities (lines 30-36)
Choices B and C are incorrect because they are not supported by inorma-
tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do
not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo
QUESTION 42
Choice C is the best answer When discussing problems with bee colo-
nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo
(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-
tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a
tentative tone and provides urther evidence that the authors believe but are
not certain that their hypothesis is correct
Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone
QUESTION 43
Choice C is the best answer In lines 24-28 the authors hypothesize that bee
colonies will be susceptible to mite inestations i they do not occasionally
eed on pyrethrum producing plants In lines 42-46 they suggest creating a
trial where a ldquosmall number o commercial honey bee colonies are offered a
number o pyrethrum producing plantsrdquo to test their hypothesis
Choices A B and D are incorrect because the authors do not hypothesize that
honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees
to develop secondary inections that beekeepers should increase their use o
insecticides or that humans are more susceptible to varroa mites
QUESTION 44
Choice D is the best answer In lines 24-28 the authors provide evidence
that a bee colony may be more resistant to mite inections i the bees eat
pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-
nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees
Choices A B and C do not describe any o the authorsrsquo hypotheses
QUESTION 45
Choice D is the best answer Te authors explain that when beekeepers
use commercially produced insecticides to fight mite inections they may
ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-
cientrdquo (lines 31-35)
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1340
12
Choices A B and C are incorrect because the authors do not suggest that
beekeepersrsquo use o commercially produced insecticides increases mite popu-
lations kills bacteria or destroys beesrsquo primary ood source
QUESTION 46
Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-
ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo
Choices A B and D are incorrect because they do not provide the best evi-
dence that beekeepersrsquo use o commercially produced insecticides may be
harmul to bees choices A B and D ocus on mite inestationsrsquo impact on
honeybees
QUESTION 47
Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some
bees Te authors then state ldquoWe urther postulate that the proper dosage
necessary to prevent mite inestation may be better lef to the beesrdquo (lines
35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the
bees may naturally control mite inestations better than insecticides
Choices A C and D are incorrect because in this context ldquopostulaterdquo does
not mean to make an unounded assumption question a belie or theory or
conclude based on firm evidence
QUESTION 48
Choice B is the best answer In the ourth paragraph the authors propose
a trial to study i honeybeesrsquo consumption o pyrethrum producing plants
helps the honeybees deend against mite inestations In the experiment the
authors plan to offer honey bee colonies both pyrethrum producing plants
and ldquoa typical bee ood source such as cloverrdquo to determine i these different
diets affect the beesrsquo susceptibility to mite inestations
Choices A C and D are incorrect because the main purpose o the ourth
paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished
experiment
QUESTION 49
Choice A is the best answer In lines 43-45 the authors propose a scien-
tific trial in which honeybees are ldquooffered a number o pyrethrum producing
plants as well as a typical bee ood source such as cloverrdquo Since the authors
contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood
sourcerdquo it can be assumed that clover does not produce pyrethrums
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1440
13
Choice B is incorrect because it is stated in the passage Choices C and D are
incorrect because they are not assumptions made by the authors
QUESTION 50
Choice B is the best answer Te table shows that 77 percent o the honeybee
colonies with colony collapse disorder were inected by all our pathogens
Choices A C and D are incorrect because they do not identiy the percent
o honeybee colonies with colony collapse disorder that were inected by all
our pathogens as based on data in the table
QUESTION 51
Choice D is the best answer Te table shows that 81 percent o colo-
nies without colony collapse disorder were affected by the pathogen
Nosema ceranae
Choices A B and C are incorrect because they do not identiy the pathogen
that inected the highest percentage o honeybee colonies without colony
collapse disorder as based on data in the table
QUESTION 52
Choice D is the best answer Te table discusses pathogen occurrence in
honeybee colonies but it includes no inormation as to whether these hon-
eybees were inected with mites Because the table does not suggest mites
inested the honeybee colonies no conclusions can be made as to whether
mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)
Choices A B and C are incorrect because the table provides no inormation
about whether these honeybees were inected with mites
Section 2 Writing and Language Test
QUESTION 1
Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-
ates a parallel structure within the list that begins with ldquohappierrdquo
Choices B C and D are incorrect because none creates a parallel structure
within the list o qualities
QUESTION 2
Choice B is the best answer Te ways in which exposure to natural light
affects employees is the main subject o the passage
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1540
14
Choices A C and D are incorrect because none introduces the topic dis-
cussed in the remainder o the passage
QUESTION 3
Choice C is the best answer It accurately notes that the proposed sentence
would be placed directly between the first mention o circadian rhythms andthe explanation o the term
Choices A B and D are incorrect because each misinterprets the relation-
ship between the proposed additional text and the ideas in the paragraph
QUESTION 4
Choice C is the best answer It provides the correct possessive construction
or ldquobodyrdquo which must be a singular noun when discussed in general terms
as in this sentence Choice C also provides the correct plural construction
or ldquoclocksrdquo
Choices A B and D are incorrect because each applies either a possessive or
a plural construction in a place where it doesnrsquot belong
QUESTION 5
Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular
noun ldquoabsenteeismrdquo
Choices B C and D are incorrect because each provides a verb that
either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy
QUESTION 6
Choice B is the best answer It contains a direct reerence to productivity
the topic introduced in the previous sentence
Choices A C and D are incorrect because none directly addresses employee
productivity the primary subject o the previous sentence
QUESTION 7
Choice A is the best answer It opens with a reerence to lowered worker
productivity creating a transition rom the previous paragraph and clearly
positions the high energy costs o artificial light sources as an additional
disadvantage
Choices B C and D are incorrect because none o the choices offer an ade-
quate transition rom the previous paragraph Each awkwardly inserts the
issue o lower worker productivity into a statement about the high energy
costs o artificial light sources
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1640
15
QUESTION 8
Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-
cate that the savings occurred every year
Choices A B and C are incorrect because each proposes an option that
would result in a redundancy with ldquoannualrdquo
QUESTION 9
Choice C is the best answer It provides a transitional adverb that accurately
communicates that this sentence describes an option that companies could
choose (ldquolight tubesrdquo) instead o the option described in the previous sen-
tence (ldquoull-pane windowsrdquo)
Choices A B and D are incorrect because each proposes a transitional
adverb that does not accurately reflect the relationship between this sen-
tence and the one preceding it
QUESTION 10
Choice C is the best answer It provides the correct relative pronoun to cor-
respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-
duce the definition that ollows
Choices A B and D are incorrect because each offers a pronoun inappropri-
ate or opening a dependent clause defining ldquolight tubesrdquo
QUESTION 11
Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the
noun ldquomeansrdquo particularly as a way to connect it to another noun or verb
Choices A C and D are incorrect because each results in nonstandard
phrasing with ldquomeansrdquo
QUESTION 12
Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-
responds with the plural noun ldquosettlersrdquo
Choices B C and D are incorrect because each provides either a nonstan-
dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo
QUESTION 13
Choice C is the best answer It creates a transition rom the poor ood qual-
ity mentioned in the previous sentence to the inormation about Harvey in
the remainder o the sentence
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1740
16
Choices A B and D are incorrect because none offers a transition rom the
previous sentence or a detail that corresponds precisely with the inorma-
tion in the remainder o the sentence
QUESTION 14
Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens
with a comma
Choices A B and C are incorrect because each proposes punctuation that
creates an inappropriately strong separation between the subject ldquoFred
Harveyrdquo and the verb ldquodecidedrdquo
QUESTION 15
Choice B is the best answer It provides the plural verb and plural posses-
sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo
Choices A C and D are incorrect because each either ails to provide a verb
that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide
the appropriate possessive pronoun
QUESTION 16
Choice C is the best answer It accurately echoes an earlier characterization
o the ood as being o ldquoterrible qualityrdquo while maintaining the established
tone o the passage
Choices A B and D are incorrect either because the word is less ormal than
the established tone o the passage (ldquoickyrdquo) or because it illogically attributes
agency to ood (ldquosinisterrdquo ldquosurlyrdquo)
QUESTION 17
Choice C is the best answer It accurately interprets ldquonot content to ollow
conventional business practicesrdquo as logically introducing the new practice o
ldquoemploying womenrdquo described in the ollowing sentences
Choices A B and D are incorrect because none recognizes why the sentence
is relevant to this particular location in the passage
QUESTION 18
Choice B is the best answer It is concise and ree o redundancies
Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and
ldquotremendousrdquo adjectives so close in meaning that together they present a
redundancy
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840
17
QUESTION 19
Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary
reerence to ldquosuch regulationsrdquo in the previous clause
Choices A B and C are incorrect because each lacks a necessary subject
such as a pronoun or noun
QUESTION 20
Choice C is the best answer It reers directly to benefits or the restaurantsrsquo
emale employees the subject o the previous sentence
Choices A B and D are incorrect because none logically builds upon the
sentence that precedes it
QUESTION 21
Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo
Choices A B and C are incorrect because each uses the punctuation or
a dependent clause (ldquoLiving independently and demonstrating an intense
work ethicrdquo) as i it were an independent clause
QUESTION 22
Choice A is the best answer It recognizes that the new inormation sup-
ports the previous sentencersquos claim that ldquothe Harvey Girls became known as
a transormative orcerdquo
Choices B C and D are incorrect because each misinterprets the relation-
ship between the proposed text and the passage
QUESTION 23
Choice A is the best answer It opens with a clause that identifies how
1-MCP affects apples which ocuses the sentence on 1-MCP as the subject
and allows the ideas in the sentence to progress logically
Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy
QUESTION 24
Choice D is the best answer Only the comma is necessary to separate
ldquoethylenerdquo rom the appositive noun phrase that defines it
Choices A B and C are incorrect because each creates a comma splice and
or adds unnecessary words
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1940
18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040
19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140
20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240
21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340
22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440
23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640
25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940
28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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4
QUESTION 12
Choice C is the best answer Te author notes that in North America ldquohopping
in a car almost always gets you to your destination more quicklyrdquo (lines 32-34)
Tis statement suggests that speed is one advantage to driving in North America
Choices A B and D are incorrect because the author does not cite environmen-
tal impact convenience or cost as advantages o driving in North America
QUESTION 13
Choice D is the best answer In lines 32-34 the author provides evidence
that speed is one advantage to driving in North America because driving
ldquoalmost always gets you to your destination more quicklyrdquo
Choices A B and C do not provide the best evidence that speed is one
advantage to driving in North America Choices A and B are incorrect
because they offer general inormation about using public transportationChoice C is incorrect because although these lines mention North America
they ocus on the disadvantages o public transportation
QUESTION 14
Choice B is the best answer Te author argues in the ourth paragraph that
public transportation ldquocan be aster more comortable and cheaper than the
private automobilerdquo (lines 36-37) and provides examples o ast and conve-
nient public transportation systems
Choices A C and D are incorrect because they ocus on points made in theourth paragraph rather than the paragraphrsquos central idea
QUESTION 15
Choice B is the best answer In lines 35-37 the author provides evidence
that some public transportation systems are superior to driving because
public transportation ldquocan be aster more comortable and cheaper than the
private automobilerdquo
Choices A C and D do not provide the best evidence that some public
transportation systems are superior to driving as they highlight points madein the ourth paragraph rather than the paragraphrsquos central idea
QUESTION 16
Choice C is the best answer In the last paragraph the author explains the
trend that people who became adults around the end o the twentieth cen-
tury are more willing to use public transportation than people rom older
generations Te author notes ldquoI you credit the demographers this transit
trend has legsrdquo (lines 58-59) In this context ldquocreditrdquo means to believe the
demographersrsquo claims about the trend
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 640
5
Choices A B and D are incorrect because in this context ldquocreditrdquo does not
mean endow attribute or honor
QUESTION 17
Choice B is the best answer In lines 59-63 the author explains the trend
o people who became adults around the end o the twentieth centuryldquotend[ing] to avor cities over suburbsrdquo In this context these adults ldquoavorrdquo
or preer cities over suburbs
Choices A C and D are incorrect because in this context ldquoavorrdquo does not
mean indulge resemble or serve
QUESTION 18
Choice B is the best answer In lines 63-67 the author explains that while
riding on public transportation people can use personal electronic devices
such as ldquoiPads MP3 players Kindles and smartphonesrdquo
Choices A C and D are incorrect because they do not show that public
transportation is compatible with the use o personal electronic devices
QUESTION 19
Choice A is the best answer Figure 1 shows that 107 o public transpor-
tation passengers are students and 67 o public transportation passengers
are retirees Tus more students than retirees use public transportation
Choices B and C are incorrect because figure 1 shows that more employedthan unemployed people use public transportation and that more employed
people than homemakers use public transportation Choice D is incorrect
because figure 1 does not explain how requently passengers use public
transportation it only identifies public transportation passengers by their
primary occupation
QUESTION 20
Choice A is the best answer Figure 1 shows that 72 o public transporta-
tion passengers are ldquoemployed outside the homerdquo and figure 2 indicates that
591 o public transportation trips are or ldquoworkrdquo It can be inerred romthese figures that many public transportation passengers take public trans-
portation to their place o employment
Choices B C and D are incorrect because figure 1 and figure 2 do not
indicate that public transportation passengers primarily use the system to
run errands use their own car on weekends or are planning to purchase
a car
7262019 PrepScholar Sat Practice Test 3 Answers
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6
QUESTION 21
Choice D is the best answer Te author explains that Ken Dial created an
experiment to study the evolution o flight by observing how baby Chukars
learn to fly During the experiment Dial noticed the unusual way Chukars
use their ldquolsquowings and legs cooperativelyrsquordquo to scale hay bales (lines 38-43) and
he created ldquoa series o ingenious experimentsrdquo (line 46) to study this obser- vation Afer his additional experiments Dial determined that these baby
birds angle ldquotheir wings differently rom birds in flightrdquo (lines 49-50)
Choices A B and C are incorrect because they do not accurately reflect the
sequence o events in the passage
QUESTION 22
Choice A is the best answer In lines 6-9 the author explains that Dial was
ldquochallengedrdquo or dared by graduate students to develop ldquonew datardquo on a long-
standing scientific debate (the ldquoground-up-tree-downrdquo theory)
Choices B C and D are incorrect because in this context ldquochallengedrdquo does
not mean required disputed with or competed with
QUESTION 23
Choice A is the best answer Te author explains that Dial created his initial
experiment to try and create ldquonew data on the age-old ground-up-tree-down
debaterdquo and that he looked or ldquocluesrdquo in ldquohow baby game birds learned to
flyrdquo (lines 8-11) Te note at the beginning o the passage explains the ldquoage-
old ground-up-tree down debaterdquo and offers two different theories on howbirds evolved to fly Finally the last paragraph o the passage discusses WAIR
in an evolutionary context
Choices B C and D are incorrect because they do not identiy Dialrsquos central
assumption in setting up his research
QUESTION 24
Choice B is the best answer In lines 6-11 the author provides evidence that
Dialrsquos central assumption in setting up his research is that the acquisition o
flight in young birds is linked to the acquisition o flight in their ancestorsTe author notes that Dial created a project to ldquocome up with new data on
the age-old ground-up-tree-down debaterdquo
Choices A C and D do not provide the best evidence that Dialrsquos central
assumption in setting up his research is that the acquisition o flight in young
birds is linked to the acquisition o flight in their ancestors Choices A C
and D are incorrect because they ocus on Dialrsquos experiment and his obser-
vations on ground birds
7262019 PrepScholar Sat Practice Test 3 Answers
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7
QUESTION 25
Choice C is the best answer When a rancher observed Dialrsquos laboratory
setup he was ldquoincredulousrdquo that the Chukars were living on the ground and
he advised Dial to give the birds ldquosomething to climb onrdquo (lines 16-23) Tis
ldquokey piece o advicerdquo (line 14) led Dial to add hay bales to his laboratory
Dial later noticed that the Chukars were using their legs and wings to scalethe hay bales and this observation became the ocal point o his research
Choices A B and D are incorrect because the incident with the local rancher
did not serve to reveal Dialrsquos motivation or creating the project emphasize
differences in laboratory and field research or introduce a contributor to a
scientific theory
QUESTION 26
Choice C is the best answer Te author explains that Dialrsquos ldquoaha momentrdquo
came when he determined the Chukars used ldquotheir legs and wings coop-erativelyrdquo to scale the hay bales (lines 40-42) Dial then created additional
experiments to study how the birds dealt with gradually steeper inclines
ldquo[he filmed] the birds as they raced up textured ramps tilted at increasing
anglesrdquo (lines 46-48)
Choices A B and D are incorrect because Dialrsquos ldquoaha momentrdquo was not ol-
lowed by Dial teaching the birds to fly studying videos to find out why the
birds no longer hopped or consulting with other researchers
QUESTION 27
Choice B is the best answer Dial observed that as the Chukars raced up
steep ramps they ldquobegan to flaprdquo and ldquoaimed their flapping down and back-
ward using the orce to keep their eet firmly pressed against the ramprdquo
(lines 49-53) Dial determined that the position o their flapping wings acil-
itated the baby Chukarsrsquo traction on the steep ramps
Choices A C and D are incorrect because the passage does not indicate that
the Chukarsrsquo speed alternation o wing and oot movement or continual
hopping motions acilitated their traction on steep ramps
QUESTION 28
Choice B is the best answer In lines 61-63 the author explains that Dial
named his scientific finding ldquoWAIR or wing-assisted incline running and
went on to document it in a wide range o speciesrdquo In this context Dial
ldquodocumentedrdquo or recorded the existence o WAIR in numerous bird species
Choices A C and D are incorrect because in this context ldquodocumentrdquo does
not mean to portray publish or process
7262019 PrepScholar Sat Practice Test 3 Answers
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8
QUESTION 29
Choice D is the best answer In lines 70-74 the author explains that glid-
ing animals do not use a ldquoflapping flight strokerdquo or WAIR wing-assisted
incline running Since Chukars a ground bird use WAIR to help scale steep
inclines it can be reasonably inerred that gliding animals do not use WAIR
to aid in climbing slopes
Choices A B and C are incorrect because the passage does not include
inormation on gliding animalsrsquo offspring their method o locomotion or
their eeding habits
QUESTION 30
Choice D is the best answer In lines 73-75 the author provides evidence
that ldquothe flapping flight strokerdquo is ldquosomething gliding animals donrsquot dordquo
Choices A B and C do not provide the best evidence that gliding animalsdo not use a flapping stroke to aid in climbing slopes Tese choices do not
contain inormation about gliding animals
QUESTION 31
Choice B is the best answer In lines 21-24 the authors o Passage 1 state
societyrsquos ldquocommon happinessrdquo is dependent on women never becoming
involved in politics In this context the authors o Passage 1 are sug-
gesting that all members o society can have a ldquocommonrdquo or shared
happiness
Choices A C and D are incorrect because in this context ldquocommonrdquo does
not mean average coarse or similar
QUESTION 32
Choice C is the best answer In lines 25-30 the authors o Passage 1 state
that women should seek ldquogentle occupations and the cares o the homerdquo
so they can avoid perorming difficult or ldquostrenuousrdquo and unpleasant or
ldquoonerousrdquo tasks
Choices A B and D are incorrect because the authors o Passage 1 do notsuggest that running a household and raising children are rewarding or
both sexes yield less value or society or require proessional or political
skills
QUESTION 33
Choice C is the best answer In lines 25-30 the authors o Passage 1 provide
evidence that women should run households and raise children because
these roles do not require ldquostrenuous habits and onerous dutiesrdquo
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9
Choices A B and D do not provide the best evidence that running a house-
hold and raising children entail very ew activities that are difficult or
unpleasant rather these lines offer general inormation about the differ-
ences between the sexes
QUESTION 34
Choice D is the best answer In lines 41-46 Wollstonecraf argues that i
women do not receive an education ldquoto become the companion o manrdquo or
one that is comparable to menrsquos education then society will not progress in
ldquoknowledge and virtuerdquo
Choices A B and C are incorrect because Wollstonecraf does not suggest
that society can progress only i women have happiness and financial secu-
rity ollow societal rules or replace men as figures o power
QUESTION 35
Choice C is the best answer Wollstonecraf argues that women should be
granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo
(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-
enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context
Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or
intellect and allow women to consider their role in society
Choices A B and D are incorrect because in this context ldquoreasonrdquo does not
mean motive sanity or explanation
QUESTION 36
Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws
passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to
ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf
is arguing that societyrsquos leaders grant men reedoms that are denied to women
Choices B C and D are incorrect because Wollstonecraf does not claim
that societyrsquos leaders have granted reedoms that created a general reduction
in individual virtue caused arguments about happiness or ensured equality
or all people
QUESTION 37
Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-
dence that societyrsquos leaders grant reedoms that privilege men She argues
that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-
lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to
ldquocontend or their reedomrdquo
Choices A B and C do not provide the best evidence that societyrsquos leaders
grant reedoms that privilege men over women
7262019 PrepScholar Sat Practice Test 3 Answers
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10
QUESTION 38
Choice C is the best answer Wollstonecraf cites the statement made by
the authors o Passage 1 that excluding women rom political participation
is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)
Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe
abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument
by highlighting a flaw in the reasoning presented by the authors o Passage 1
Choices A B and D are incorrect because Wollstonecraf does not reer to
the statement made in Passage 1 to call into question the authorsrsquo qualifica-
tions dispute the assertion that women are excluded by their own govern-
ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on
gender roles
QUESTION 39
Choice A is the best answer Te authors o Passage 1 argue that while
restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)
this restriction is necessary or societyrsquos overall happiness (lines 13-17)
Wollstonecraf however strongly challenges this argument asking the
authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-
doms are granted to women and likening societyrsquos male leaders to tyrants as
they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in
the darkrdquo (lines 78-88)
Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2
QUESTION 40
Choice D is the best answer Te authors o Passage 1 admit that women are
ldquoexcluded by the other hal [men] rom any participation in governmentrdquo
(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws
that deny women ldquocivil and political rightsrdquo (line 86)
Choices A B and C are incorrect because the authors o both passages
would not agree that women had the same preerences as men required agood education or were as happy as men
QUESTION 41
Choice A is the best answer Wollstonecraf argues in the final paragraph
o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women
ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would
most likely argue that allowing women these rights would be ldquoa reversal o
[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos
interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as
7262019 PrepScholar Sat Practice Test 3 Answers
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11
mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created
two sexes or a particular reason so while men can exercise civil and politi-
cal rights women are not naturally suited to these activities (lines 30-36)
Choices B and C are incorrect because they are not supported by inorma-
tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do
not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo
QUESTION 42
Choice C is the best answer When discussing problems with bee colo-
nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo
(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-
tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a
tentative tone and provides urther evidence that the authors believe but are
not certain that their hypothesis is correct
Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone
QUESTION 43
Choice C is the best answer In lines 24-28 the authors hypothesize that bee
colonies will be susceptible to mite inestations i they do not occasionally
eed on pyrethrum producing plants In lines 42-46 they suggest creating a
trial where a ldquosmall number o commercial honey bee colonies are offered a
number o pyrethrum producing plantsrdquo to test their hypothesis
Choices A B and D are incorrect because the authors do not hypothesize that
honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees
to develop secondary inections that beekeepers should increase their use o
insecticides or that humans are more susceptible to varroa mites
QUESTION 44
Choice D is the best answer In lines 24-28 the authors provide evidence
that a bee colony may be more resistant to mite inections i the bees eat
pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-
nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees
Choices A B and C do not describe any o the authorsrsquo hypotheses
QUESTION 45
Choice D is the best answer Te authors explain that when beekeepers
use commercially produced insecticides to fight mite inections they may
ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-
cientrdquo (lines 31-35)
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12
Choices A B and C are incorrect because the authors do not suggest that
beekeepersrsquo use o commercially produced insecticides increases mite popu-
lations kills bacteria or destroys beesrsquo primary ood source
QUESTION 46
Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-
ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo
Choices A B and D are incorrect because they do not provide the best evi-
dence that beekeepersrsquo use o commercially produced insecticides may be
harmul to bees choices A B and D ocus on mite inestationsrsquo impact on
honeybees
QUESTION 47
Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some
bees Te authors then state ldquoWe urther postulate that the proper dosage
necessary to prevent mite inestation may be better lef to the beesrdquo (lines
35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the
bees may naturally control mite inestations better than insecticides
Choices A C and D are incorrect because in this context ldquopostulaterdquo does
not mean to make an unounded assumption question a belie or theory or
conclude based on firm evidence
QUESTION 48
Choice B is the best answer In the ourth paragraph the authors propose
a trial to study i honeybeesrsquo consumption o pyrethrum producing plants
helps the honeybees deend against mite inestations In the experiment the
authors plan to offer honey bee colonies both pyrethrum producing plants
and ldquoa typical bee ood source such as cloverrdquo to determine i these different
diets affect the beesrsquo susceptibility to mite inestations
Choices A C and D are incorrect because the main purpose o the ourth
paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished
experiment
QUESTION 49
Choice A is the best answer In lines 43-45 the authors propose a scien-
tific trial in which honeybees are ldquooffered a number o pyrethrum producing
plants as well as a typical bee ood source such as cloverrdquo Since the authors
contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood
sourcerdquo it can be assumed that clover does not produce pyrethrums
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13
Choice B is incorrect because it is stated in the passage Choices C and D are
incorrect because they are not assumptions made by the authors
QUESTION 50
Choice B is the best answer Te table shows that 77 percent o the honeybee
colonies with colony collapse disorder were inected by all our pathogens
Choices A C and D are incorrect because they do not identiy the percent
o honeybee colonies with colony collapse disorder that were inected by all
our pathogens as based on data in the table
QUESTION 51
Choice D is the best answer Te table shows that 81 percent o colo-
nies without colony collapse disorder were affected by the pathogen
Nosema ceranae
Choices A B and C are incorrect because they do not identiy the pathogen
that inected the highest percentage o honeybee colonies without colony
collapse disorder as based on data in the table
QUESTION 52
Choice D is the best answer Te table discusses pathogen occurrence in
honeybee colonies but it includes no inormation as to whether these hon-
eybees were inected with mites Because the table does not suggest mites
inested the honeybee colonies no conclusions can be made as to whether
mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)
Choices A B and C are incorrect because the table provides no inormation
about whether these honeybees were inected with mites
Section 2 Writing and Language Test
QUESTION 1
Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-
ates a parallel structure within the list that begins with ldquohappierrdquo
Choices B C and D are incorrect because none creates a parallel structure
within the list o qualities
QUESTION 2
Choice B is the best answer Te ways in which exposure to natural light
affects employees is the main subject o the passage
7262019 PrepScholar Sat Practice Test 3 Answers
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14
Choices A C and D are incorrect because none introduces the topic dis-
cussed in the remainder o the passage
QUESTION 3
Choice C is the best answer It accurately notes that the proposed sentence
would be placed directly between the first mention o circadian rhythms andthe explanation o the term
Choices A B and D are incorrect because each misinterprets the relation-
ship between the proposed additional text and the ideas in the paragraph
QUESTION 4
Choice C is the best answer It provides the correct possessive construction
or ldquobodyrdquo which must be a singular noun when discussed in general terms
as in this sentence Choice C also provides the correct plural construction
or ldquoclocksrdquo
Choices A B and D are incorrect because each applies either a possessive or
a plural construction in a place where it doesnrsquot belong
QUESTION 5
Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular
noun ldquoabsenteeismrdquo
Choices B C and D are incorrect because each provides a verb that
either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy
QUESTION 6
Choice B is the best answer It contains a direct reerence to productivity
the topic introduced in the previous sentence
Choices A C and D are incorrect because none directly addresses employee
productivity the primary subject o the previous sentence
QUESTION 7
Choice A is the best answer It opens with a reerence to lowered worker
productivity creating a transition rom the previous paragraph and clearly
positions the high energy costs o artificial light sources as an additional
disadvantage
Choices B C and D are incorrect because none o the choices offer an ade-
quate transition rom the previous paragraph Each awkwardly inserts the
issue o lower worker productivity into a statement about the high energy
costs o artificial light sources
7262019 PrepScholar Sat Practice Test 3 Answers
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15
QUESTION 8
Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-
cate that the savings occurred every year
Choices A B and C are incorrect because each proposes an option that
would result in a redundancy with ldquoannualrdquo
QUESTION 9
Choice C is the best answer It provides a transitional adverb that accurately
communicates that this sentence describes an option that companies could
choose (ldquolight tubesrdquo) instead o the option described in the previous sen-
tence (ldquoull-pane windowsrdquo)
Choices A B and D are incorrect because each proposes a transitional
adverb that does not accurately reflect the relationship between this sen-
tence and the one preceding it
QUESTION 10
Choice C is the best answer It provides the correct relative pronoun to cor-
respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-
duce the definition that ollows
Choices A B and D are incorrect because each offers a pronoun inappropri-
ate or opening a dependent clause defining ldquolight tubesrdquo
QUESTION 11
Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the
noun ldquomeansrdquo particularly as a way to connect it to another noun or verb
Choices A C and D are incorrect because each results in nonstandard
phrasing with ldquomeansrdquo
QUESTION 12
Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-
responds with the plural noun ldquosettlersrdquo
Choices B C and D are incorrect because each provides either a nonstan-
dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo
QUESTION 13
Choice C is the best answer It creates a transition rom the poor ood qual-
ity mentioned in the previous sentence to the inormation about Harvey in
the remainder o the sentence
7262019 PrepScholar Sat Practice Test 3 Answers
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16
Choices A B and D are incorrect because none offers a transition rom the
previous sentence or a detail that corresponds precisely with the inorma-
tion in the remainder o the sentence
QUESTION 14
Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens
with a comma
Choices A B and C are incorrect because each proposes punctuation that
creates an inappropriately strong separation between the subject ldquoFred
Harveyrdquo and the verb ldquodecidedrdquo
QUESTION 15
Choice B is the best answer It provides the plural verb and plural posses-
sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo
Choices A C and D are incorrect because each either ails to provide a verb
that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide
the appropriate possessive pronoun
QUESTION 16
Choice C is the best answer It accurately echoes an earlier characterization
o the ood as being o ldquoterrible qualityrdquo while maintaining the established
tone o the passage
Choices A B and D are incorrect either because the word is less ormal than
the established tone o the passage (ldquoickyrdquo) or because it illogically attributes
agency to ood (ldquosinisterrdquo ldquosurlyrdquo)
QUESTION 17
Choice C is the best answer It accurately interprets ldquonot content to ollow
conventional business practicesrdquo as logically introducing the new practice o
ldquoemploying womenrdquo described in the ollowing sentences
Choices A B and D are incorrect because none recognizes why the sentence
is relevant to this particular location in the passage
QUESTION 18
Choice B is the best answer It is concise and ree o redundancies
Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and
ldquotremendousrdquo adjectives so close in meaning that together they present a
redundancy
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840
17
QUESTION 19
Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary
reerence to ldquosuch regulationsrdquo in the previous clause
Choices A B and C are incorrect because each lacks a necessary subject
such as a pronoun or noun
QUESTION 20
Choice C is the best answer It reers directly to benefits or the restaurantsrsquo
emale employees the subject o the previous sentence
Choices A B and D are incorrect because none logically builds upon the
sentence that precedes it
QUESTION 21
Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo
Choices A B and C are incorrect because each uses the punctuation or
a dependent clause (ldquoLiving independently and demonstrating an intense
work ethicrdquo) as i it were an independent clause
QUESTION 22
Choice A is the best answer It recognizes that the new inormation sup-
ports the previous sentencersquos claim that ldquothe Harvey Girls became known as
a transormative orcerdquo
Choices B C and D are incorrect because each misinterprets the relation-
ship between the proposed text and the passage
QUESTION 23
Choice A is the best answer It opens with a clause that identifies how
1-MCP affects apples which ocuses the sentence on 1-MCP as the subject
and allows the ideas in the sentence to progress logically
Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy
QUESTION 24
Choice D is the best answer Only the comma is necessary to separate
ldquoethylenerdquo rom the appositive noun phrase that defines it
Choices A B and C are incorrect because each creates a comma splice and
or adds unnecessary words
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1940
18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040
19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140
20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240
21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340
22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440
23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640
25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940
28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040
29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3340
32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3440
33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3540
34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640
35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740
36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3940
38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 640
5
Choices A B and D are incorrect because in this context ldquocreditrdquo does not
mean endow attribute or honor
QUESTION 17
Choice B is the best answer In lines 59-63 the author explains the trend
o people who became adults around the end o the twentieth centuryldquotend[ing] to avor cities over suburbsrdquo In this context these adults ldquoavorrdquo
or preer cities over suburbs
Choices A C and D are incorrect because in this context ldquoavorrdquo does not
mean indulge resemble or serve
QUESTION 18
Choice B is the best answer In lines 63-67 the author explains that while
riding on public transportation people can use personal electronic devices
such as ldquoiPads MP3 players Kindles and smartphonesrdquo
Choices A C and D are incorrect because they do not show that public
transportation is compatible with the use o personal electronic devices
QUESTION 19
Choice A is the best answer Figure 1 shows that 107 o public transpor-
tation passengers are students and 67 o public transportation passengers
are retirees Tus more students than retirees use public transportation
Choices B and C are incorrect because figure 1 shows that more employedthan unemployed people use public transportation and that more employed
people than homemakers use public transportation Choice D is incorrect
because figure 1 does not explain how requently passengers use public
transportation it only identifies public transportation passengers by their
primary occupation
QUESTION 20
Choice A is the best answer Figure 1 shows that 72 o public transporta-
tion passengers are ldquoemployed outside the homerdquo and figure 2 indicates that
591 o public transportation trips are or ldquoworkrdquo It can be inerred romthese figures that many public transportation passengers take public trans-
portation to their place o employment
Choices B C and D are incorrect because figure 1 and figure 2 do not
indicate that public transportation passengers primarily use the system to
run errands use their own car on weekends or are planning to purchase
a car
7262019 PrepScholar Sat Practice Test 3 Answers
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6
QUESTION 21
Choice D is the best answer Te author explains that Ken Dial created an
experiment to study the evolution o flight by observing how baby Chukars
learn to fly During the experiment Dial noticed the unusual way Chukars
use their ldquolsquowings and legs cooperativelyrsquordquo to scale hay bales (lines 38-43) and
he created ldquoa series o ingenious experimentsrdquo (line 46) to study this obser- vation Afer his additional experiments Dial determined that these baby
birds angle ldquotheir wings differently rom birds in flightrdquo (lines 49-50)
Choices A B and C are incorrect because they do not accurately reflect the
sequence o events in the passage
QUESTION 22
Choice A is the best answer In lines 6-9 the author explains that Dial was
ldquochallengedrdquo or dared by graduate students to develop ldquonew datardquo on a long-
standing scientific debate (the ldquoground-up-tree-downrdquo theory)
Choices B C and D are incorrect because in this context ldquochallengedrdquo does
not mean required disputed with or competed with
QUESTION 23
Choice A is the best answer Te author explains that Dial created his initial
experiment to try and create ldquonew data on the age-old ground-up-tree-down
debaterdquo and that he looked or ldquocluesrdquo in ldquohow baby game birds learned to
flyrdquo (lines 8-11) Te note at the beginning o the passage explains the ldquoage-
old ground-up-tree down debaterdquo and offers two different theories on howbirds evolved to fly Finally the last paragraph o the passage discusses WAIR
in an evolutionary context
Choices B C and D are incorrect because they do not identiy Dialrsquos central
assumption in setting up his research
QUESTION 24
Choice B is the best answer In lines 6-11 the author provides evidence that
Dialrsquos central assumption in setting up his research is that the acquisition o
flight in young birds is linked to the acquisition o flight in their ancestorsTe author notes that Dial created a project to ldquocome up with new data on
the age-old ground-up-tree-down debaterdquo
Choices A C and D do not provide the best evidence that Dialrsquos central
assumption in setting up his research is that the acquisition o flight in young
birds is linked to the acquisition o flight in their ancestors Choices A C
and D are incorrect because they ocus on Dialrsquos experiment and his obser-
vations on ground birds
7262019 PrepScholar Sat Practice Test 3 Answers
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7
QUESTION 25
Choice C is the best answer When a rancher observed Dialrsquos laboratory
setup he was ldquoincredulousrdquo that the Chukars were living on the ground and
he advised Dial to give the birds ldquosomething to climb onrdquo (lines 16-23) Tis
ldquokey piece o advicerdquo (line 14) led Dial to add hay bales to his laboratory
Dial later noticed that the Chukars were using their legs and wings to scalethe hay bales and this observation became the ocal point o his research
Choices A B and D are incorrect because the incident with the local rancher
did not serve to reveal Dialrsquos motivation or creating the project emphasize
differences in laboratory and field research or introduce a contributor to a
scientific theory
QUESTION 26
Choice C is the best answer Te author explains that Dialrsquos ldquoaha momentrdquo
came when he determined the Chukars used ldquotheir legs and wings coop-erativelyrdquo to scale the hay bales (lines 40-42) Dial then created additional
experiments to study how the birds dealt with gradually steeper inclines
ldquo[he filmed] the birds as they raced up textured ramps tilted at increasing
anglesrdquo (lines 46-48)
Choices A B and D are incorrect because Dialrsquos ldquoaha momentrdquo was not ol-
lowed by Dial teaching the birds to fly studying videos to find out why the
birds no longer hopped or consulting with other researchers
QUESTION 27
Choice B is the best answer Dial observed that as the Chukars raced up
steep ramps they ldquobegan to flaprdquo and ldquoaimed their flapping down and back-
ward using the orce to keep their eet firmly pressed against the ramprdquo
(lines 49-53) Dial determined that the position o their flapping wings acil-
itated the baby Chukarsrsquo traction on the steep ramps
Choices A C and D are incorrect because the passage does not indicate that
the Chukarsrsquo speed alternation o wing and oot movement or continual
hopping motions acilitated their traction on steep ramps
QUESTION 28
Choice B is the best answer In lines 61-63 the author explains that Dial
named his scientific finding ldquoWAIR or wing-assisted incline running and
went on to document it in a wide range o speciesrdquo In this context Dial
ldquodocumentedrdquo or recorded the existence o WAIR in numerous bird species
Choices A C and D are incorrect because in this context ldquodocumentrdquo does
not mean to portray publish or process
7262019 PrepScholar Sat Practice Test 3 Answers
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8
QUESTION 29
Choice D is the best answer In lines 70-74 the author explains that glid-
ing animals do not use a ldquoflapping flight strokerdquo or WAIR wing-assisted
incline running Since Chukars a ground bird use WAIR to help scale steep
inclines it can be reasonably inerred that gliding animals do not use WAIR
to aid in climbing slopes
Choices A B and C are incorrect because the passage does not include
inormation on gliding animalsrsquo offspring their method o locomotion or
their eeding habits
QUESTION 30
Choice D is the best answer In lines 73-75 the author provides evidence
that ldquothe flapping flight strokerdquo is ldquosomething gliding animals donrsquot dordquo
Choices A B and C do not provide the best evidence that gliding animalsdo not use a flapping stroke to aid in climbing slopes Tese choices do not
contain inormation about gliding animals
QUESTION 31
Choice B is the best answer In lines 21-24 the authors o Passage 1 state
societyrsquos ldquocommon happinessrdquo is dependent on women never becoming
involved in politics In this context the authors o Passage 1 are sug-
gesting that all members o society can have a ldquocommonrdquo or shared
happiness
Choices A C and D are incorrect because in this context ldquocommonrdquo does
not mean average coarse or similar
QUESTION 32
Choice C is the best answer In lines 25-30 the authors o Passage 1 state
that women should seek ldquogentle occupations and the cares o the homerdquo
so they can avoid perorming difficult or ldquostrenuousrdquo and unpleasant or
ldquoonerousrdquo tasks
Choices A B and D are incorrect because the authors o Passage 1 do notsuggest that running a household and raising children are rewarding or
both sexes yield less value or society or require proessional or political
skills
QUESTION 33
Choice C is the best answer In lines 25-30 the authors o Passage 1 provide
evidence that women should run households and raise children because
these roles do not require ldquostrenuous habits and onerous dutiesrdquo
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9
Choices A B and D do not provide the best evidence that running a house-
hold and raising children entail very ew activities that are difficult or
unpleasant rather these lines offer general inormation about the differ-
ences between the sexes
QUESTION 34
Choice D is the best answer In lines 41-46 Wollstonecraf argues that i
women do not receive an education ldquoto become the companion o manrdquo or
one that is comparable to menrsquos education then society will not progress in
ldquoknowledge and virtuerdquo
Choices A B and C are incorrect because Wollstonecraf does not suggest
that society can progress only i women have happiness and financial secu-
rity ollow societal rules or replace men as figures o power
QUESTION 35
Choice C is the best answer Wollstonecraf argues that women should be
granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo
(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-
enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context
Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or
intellect and allow women to consider their role in society
Choices A B and D are incorrect because in this context ldquoreasonrdquo does not
mean motive sanity or explanation
QUESTION 36
Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws
passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to
ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf
is arguing that societyrsquos leaders grant men reedoms that are denied to women
Choices B C and D are incorrect because Wollstonecraf does not claim
that societyrsquos leaders have granted reedoms that created a general reduction
in individual virtue caused arguments about happiness or ensured equality
or all people
QUESTION 37
Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-
dence that societyrsquos leaders grant reedoms that privilege men She argues
that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-
lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to
ldquocontend or their reedomrdquo
Choices A B and C do not provide the best evidence that societyrsquos leaders
grant reedoms that privilege men over women
7262019 PrepScholar Sat Practice Test 3 Answers
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10
QUESTION 38
Choice C is the best answer Wollstonecraf cites the statement made by
the authors o Passage 1 that excluding women rom political participation
is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)
Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe
abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument
by highlighting a flaw in the reasoning presented by the authors o Passage 1
Choices A B and D are incorrect because Wollstonecraf does not reer to
the statement made in Passage 1 to call into question the authorsrsquo qualifica-
tions dispute the assertion that women are excluded by their own govern-
ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on
gender roles
QUESTION 39
Choice A is the best answer Te authors o Passage 1 argue that while
restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)
this restriction is necessary or societyrsquos overall happiness (lines 13-17)
Wollstonecraf however strongly challenges this argument asking the
authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-
doms are granted to women and likening societyrsquos male leaders to tyrants as
they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in
the darkrdquo (lines 78-88)
Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2
QUESTION 40
Choice D is the best answer Te authors o Passage 1 admit that women are
ldquoexcluded by the other hal [men] rom any participation in governmentrdquo
(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws
that deny women ldquocivil and political rightsrdquo (line 86)
Choices A B and C are incorrect because the authors o both passages
would not agree that women had the same preerences as men required agood education or were as happy as men
QUESTION 41
Choice A is the best answer Wollstonecraf argues in the final paragraph
o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women
ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would
most likely argue that allowing women these rights would be ldquoa reversal o
[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos
interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as
7262019 PrepScholar Sat Practice Test 3 Answers
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11
mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created
two sexes or a particular reason so while men can exercise civil and politi-
cal rights women are not naturally suited to these activities (lines 30-36)
Choices B and C are incorrect because they are not supported by inorma-
tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do
not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo
QUESTION 42
Choice C is the best answer When discussing problems with bee colo-
nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo
(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-
tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a
tentative tone and provides urther evidence that the authors believe but are
not certain that their hypothesis is correct
Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone
QUESTION 43
Choice C is the best answer In lines 24-28 the authors hypothesize that bee
colonies will be susceptible to mite inestations i they do not occasionally
eed on pyrethrum producing plants In lines 42-46 they suggest creating a
trial where a ldquosmall number o commercial honey bee colonies are offered a
number o pyrethrum producing plantsrdquo to test their hypothesis
Choices A B and D are incorrect because the authors do not hypothesize that
honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees
to develop secondary inections that beekeepers should increase their use o
insecticides or that humans are more susceptible to varroa mites
QUESTION 44
Choice D is the best answer In lines 24-28 the authors provide evidence
that a bee colony may be more resistant to mite inections i the bees eat
pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-
nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees
Choices A B and C do not describe any o the authorsrsquo hypotheses
QUESTION 45
Choice D is the best answer Te authors explain that when beekeepers
use commercially produced insecticides to fight mite inections they may
ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-
cientrdquo (lines 31-35)
7262019 PrepScholar Sat Practice Test 3 Answers
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12
Choices A B and C are incorrect because the authors do not suggest that
beekeepersrsquo use o commercially produced insecticides increases mite popu-
lations kills bacteria or destroys beesrsquo primary ood source
QUESTION 46
Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-
ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo
Choices A B and D are incorrect because they do not provide the best evi-
dence that beekeepersrsquo use o commercially produced insecticides may be
harmul to bees choices A B and D ocus on mite inestationsrsquo impact on
honeybees
QUESTION 47
Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some
bees Te authors then state ldquoWe urther postulate that the proper dosage
necessary to prevent mite inestation may be better lef to the beesrdquo (lines
35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the
bees may naturally control mite inestations better than insecticides
Choices A C and D are incorrect because in this context ldquopostulaterdquo does
not mean to make an unounded assumption question a belie or theory or
conclude based on firm evidence
QUESTION 48
Choice B is the best answer In the ourth paragraph the authors propose
a trial to study i honeybeesrsquo consumption o pyrethrum producing plants
helps the honeybees deend against mite inestations In the experiment the
authors plan to offer honey bee colonies both pyrethrum producing plants
and ldquoa typical bee ood source such as cloverrdquo to determine i these different
diets affect the beesrsquo susceptibility to mite inestations
Choices A C and D are incorrect because the main purpose o the ourth
paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished
experiment
QUESTION 49
Choice A is the best answer In lines 43-45 the authors propose a scien-
tific trial in which honeybees are ldquooffered a number o pyrethrum producing
plants as well as a typical bee ood source such as cloverrdquo Since the authors
contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood
sourcerdquo it can be assumed that clover does not produce pyrethrums
7262019 PrepScholar Sat Practice Test 3 Answers
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13
Choice B is incorrect because it is stated in the passage Choices C and D are
incorrect because they are not assumptions made by the authors
QUESTION 50
Choice B is the best answer Te table shows that 77 percent o the honeybee
colonies with colony collapse disorder were inected by all our pathogens
Choices A C and D are incorrect because they do not identiy the percent
o honeybee colonies with colony collapse disorder that were inected by all
our pathogens as based on data in the table
QUESTION 51
Choice D is the best answer Te table shows that 81 percent o colo-
nies without colony collapse disorder were affected by the pathogen
Nosema ceranae
Choices A B and C are incorrect because they do not identiy the pathogen
that inected the highest percentage o honeybee colonies without colony
collapse disorder as based on data in the table
QUESTION 52
Choice D is the best answer Te table discusses pathogen occurrence in
honeybee colonies but it includes no inormation as to whether these hon-
eybees were inected with mites Because the table does not suggest mites
inested the honeybee colonies no conclusions can be made as to whether
mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)
Choices A B and C are incorrect because the table provides no inormation
about whether these honeybees were inected with mites
Section 2 Writing and Language Test
QUESTION 1
Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-
ates a parallel structure within the list that begins with ldquohappierrdquo
Choices B C and D are incorrect because none creates a parallel structure
within the list o qualities
QUESTION 2
Choice B is the best answer Te ways in which exposure to natural light
affects employees is the main subject o the passage
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14
Choices A C and D are incorrect because none introduces the topic dis-
cussed in the remainder o the passage
QUESTION 3
Choice C is the best answer It accurately notes that the proposed sentence
would be placed directly between the first mention o circadian rhythms andthe explanation o the term
Choices A B and D are incorrect because each misinterprets the relation-
ship between the proposed additional text and the ideas in the paragraph
QUESTION 4
Choice C is the best answer It provides the correct possessive construction
or ldquobodyrdquo which must be a singular noun when discussed in general terms
as in this sentence Choice C also provides the correct plural construction
or ldquoclocksrdquo
Choices A B and D are incorrect because each applies either a possessive or
a plural construction in a place where it doesnrsquot belong
QUESTION 5
Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular
noun ldquoabsenteeismrdquo
Choices B C and D are incorrect because each provides a verb that
either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy
QUESTION 6
Choice B is the best answer It contains a direct reerence to productivity
the topic introduced in the previous sentence
Choices A C and D are incorrect because none directly addresses employee
productivity the primary subject o the previous sentence
QUESTION 7
Choice A is the best answer It opens with a reerence to lowered worker
productivity creating a transition rom the previous paragraph and clearly
positions the high energy costs o artificial light sources as an additional
disadvantage
Choices B C and D are incorrect because none o the choices offer an ade-
quate transition rom the previous paragraph Each awkwardly inserts the
issue o lower worker productivity into a statement about the high energy
costs o artificial light sources
7262019 PrepScholar Sat Practice Test 3 Answers
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15
QUESTION 8
Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-
cate that the savings occurred every year
Choices A B and C are incorrect because each proposes an option that
would result in a redundancy with ldquoannualrdquo
QUESTION 9
Choice C is the best answer It provides a transitional adverb that accurately
communicates that this sentence describes an option that companies could
choose (ldquolight tubesrdquo) instead o the option described in the previous sen-
tence (ldquoull-pane windowsrdquo)
Choices A B and D are incorrect because each proposes a transitional
adverb that does not accurately reflect the relationship between this sen-
tence and the one preceding it
QUESTION 10
Choice C is the best answer It provides the correct relative pronoun to cor-
respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-
duce the definition that ollows
Choices A B and D are incorrect because each offers a pronoun inappropri-
ate or opening a dependent clause defining ldquolight tubesrdquo
QUESTION 11
Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the
noun ldquomeansrdquo particularly as a way to connect it to another noun or verb
Choices A C and D are incorrect because each results in nonstandard
phrasing with ldquomeansrdquo
QUESTION 12
Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-
responds with the plural noun ldquosettlersrdquo
Choices B C and D are incorrect because each provides either a nonstan-
dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo
QUESTION 13
Choice C is the best answer It creates a transition rom the poor ood qual-
ity mentioned in the previous sentence to the inormation about Harvey in
the remainder o the sentence
7262019 PrepScholar Sat Practice Test 3 Answers
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16
Choices A B and D are incorrect because none offers a transition rom the
previous sentence or a detail that corresponds precisely with the inorma-
tion in the remainder o the sentence
QUESTION 14
Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens
with a comma
Choices A B and C are incorrect because each proposes punctuation that
creates an inappropriately strong separation between the subject ldquoFred
Harveyrdquo and the verb ldquodecidedrdquo
QUESTION 15
Choice B is the best answer It provides the plural verb and plural posses-
sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo
Choices A C and D are incorrect because each either ails to provide a verb
that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide
the appropriate possessive pronoun
QUESTION 16
Choice C is the best answer It accurately echoes an earlier characterization
o the ood as being o ldquoterrible qualityrdquo while maintaining the established
tone o the passage
Choices A B and D are incorrect either because the word is less ormal than
the established tone o the passage (ldquoickyrdquo) or because it illogically attributes
agency to ood (ldquosinisterrdquo ldquosurlyrdquo)
QUESTION 17
Choice C is the best answer It accurately interprets ldquonot content to ollow
conventional business practicesrdquo as logically introducing the new practice o
ldquoemploying womenrdquo described in the ollowing sentences
Choices A B and D are incorrect because none recognizes why the sentence
is relevant to this particular location in the passage
QUESTION 18
Choice B is the best answer It is concise and ree o redundancies
Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and
ldquotremendousrdquo adjectives so close in meaning that together they present a
redundancy
7262019 PrepScholar Sat Practice Test 3 Answers
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17
QUESTION 19
Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary
reerence to ldquosuch regulationsrdquo in the previous clause
Choices A B and C are incorrect because each lacks a necessary subject
such as a pronoun or noun
QUESTION 20
Choice C is the best answer It reers directly to benefits or the restaurantsrsquo
emale employees the subject o the previous sentence
Choices A B and D are incorrect because none logically builds upon the
sentence that precedes it
QUESTION 21
Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo
Choices A B and C are incorrect because each uses the punctuation or
a dependent clause (ldquoLiving independently and demonstrating an intense
work ethicrdquo) as i it were an independent clause
QUESTION 22
Choice A is the best answer It recognizes that the new inormation sup-
ports the previous sentencersquos claim that ldquothe Harvey Girls became known as
a transormative orcerdquo
Choices B C and D are incorrect because each misinterprets the relation-
ship between the proposed text and the passage
QUESTION 23
Choice A is the best answer It opens with a clause that identifies how
1-MCP affects apples which ocuses the sentence on 1-MCP as the subject
and allows the ideas in the sentence to progress logically
Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy
QUESTION 24
Choice D is the best answer Only the comma is necessary to separate
ldquoethylenerdquo rom the appositive noun phrase that defines it
Choices A B and C are incorrect because each creates a comma splice and
or adds unnecessary words
7262019 PrepScholar Sat Practice Test 3 Answers
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18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
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19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340
22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440
23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
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25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
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26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
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28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040
29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3140
30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3440
33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3540
34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640
35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740
36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3840
37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3940
38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040
QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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6
QUESTION 21
Choice D is the best answer Te author explains that Ken Dial created an
experiment to study the evolution o flight by observing how baby Chukars
learn to fly During the experiment Dial noticed the unusual way Chukars
use their ldquolsquowings and legs cooperativelyrsquordquo to scale hay bales (lines 38-43) and
he created ldquoa series o ingenious experimentsrdquo (line 46) to study this obser- vation Afer his additional experiments Dial determined that these baby
birds angle ldquotheir wings differently rom birds in flightrdquo (lines 49-50)
Choices A B and C are incorrect because they do not accurately reflect the
sequence o events in the passage
QUESTION 22
Choice A is the best answer In lines 6-9 the author explains that Dial was
ldquochallengedrdquo or dared by graduate students to develop ldquonew datardquo on a long-
standing scientific debate (the ldquoground-up-tree-downrdquo theory)
Choices B C and D are incorrect because in this context ldquochallengedrdquo does
not mean required disputed with or competed with
QUESTION 23
Choice A is the best answer Te author explains that Dial created his initial
experiment to try and create ldquonew data on the age-old ground-up-tree-down
debaterdquo and that he looked or ldquocluesrdquo in ldquohow baby game birds learned to
flyrdquo (lines 8-11) Te note at the beginning o the passage explains the ldquoage-
old ground-up-tree down debaterdquo and offers two different theories on howbirds evolved to fly Finally the last paragraph o the passage discusses WAIR
in an evolutionary context
Choices B C and D are incorrect because they do not identiy Dialrsquos central
assumption in setting up his research
QUESTION 24
Choice B is the best answer In lines 6-11 the author provides evidence that
Dialrsquos central assumption in setting up his research is that the acquisition o
flight in young birds is linked to the acquisition o flight in their ancestorsTe author notes that Dial created a project to ldquocome up with new data on
the age-old ground-up-tree-down debaterdquo
Choices A C and D do not provide the best evidence that Dialrsquos central
assumption in setting up his research is that the acquisition o flight in young
birds is linked to the acquisition o flight in their ancestors Choices A C
and D are incorrect because they ocus on Dialrsquos experiment and his obser-
vations on ground birds
7262019 PrepScholar Sat Practice Test 3 Answers
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7
QUESTION 25
Choice C is the best answer When a rancher observed Dialrsquos laboratory
setup he was ldquoincredulousrdquo that the Chukars were living on the ground and
he advised Dial to give the birds ldquosomething to climb onrdquo (lines 16-23) Tis
ldquokey piece o advicerdquo (line 14) led Dial to add hay bales to his laboratory
Dial later noticed that the Chukars were using their legs and wings to scalethe hay bales and this observation became the ocal point o his research
Choices A B and D are incorrect because the incident with the local rancher
did not serve to reveal Dialrsquos motivation or creating the project emphasize
differences in laboratory and field research or introduce a contributor to a
scientific theory
QUESTION 26
Choice C is the best answer Te author explains that Dialrsquos ldquoaha momentrdquo
came when he determined the Chukars used ldquotheir legs and wings coop-erativelyrdquo to scale the hay bales (lines 40-42) Dial then created additional
experiments to study how the birds dealt with gradually steeper inclines
ldquo[he filmed] the birds as they raced up textured ramps tilted at increasing
anglesrdquo (lines 46-48)
Choices A B and D are incorrect because Dialrsquos ldquoaha momentrdquo was not ol-
lowed by Dial teaching the birds to fly studying videos to find out why the
birds no longer hopped or consulting with other researchers
QUESTION 27
Choice B is the best answer Dial observed that as the Chukars raced up
steep ramps they ldquobegan to flaprdquo and ldquoaimed their flapping down and back-
ward using the orce to keep their eet firmly pressed against the ramprdquo
(lines 49-53) Dial determined that the position o their flapping wings acil-
itated the baby Chukarsrsquo traction on the steep ramps
Choices A C and D are incorrect because the passage does not indicate that
the Chukarsrsquo speed alternation o wing and oot movement or continual
hopping motions acilitated their traction on steep ramps
QUESTION 28
Choice B is the best answer In lines 61-63 the author explains that Dial
named his scientific finding ldquoWAIR or wing-assisted incline running and
went on to document it in a wide range o speciesrdquo In this context Dial
ldquodocumentedrdquo or recorded the existence o WAIR in numerous bird species
Choices A C and D are incorrect because in this context ldquodocumentrdquo does
not mean to portray publish or process
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 940
8
QUESTION 29
Choice D is the best answer In lines 70-74 the author explains that glid-
ing animals do not use a ldquoflapping flight strokerdquo or WAIR wing-assisted
incline running Since Chukars a ground bird use WAIR to help scale steep
inclines it can be reasonably inerred that gliding animals do not use WAIR
to aid in climbing slopes
Choices A B and C are incorrect because the passage does not include
inormation on gliding animalsrsquo offspring their method o locomotion or
their eeding habits
QUESTION 30
Choice D is the best answer In lines 73-75 the author provides evidence
that ldquothe flapping flight strokerdquo is ldquosomething gliding animals donrsquot dordquo
Choices A B and C do not provide the best evidence that gliding animalsdo not use a flapping stroke to aid in climbing slopes Tese choices do not
contain inormation about gliding animals
QUESTION 31
Choice B is the best answer In lines 21-24 the authors o Passage 1 state
societyrsquos ldquocommon happinessrdquo is dependent on women never becoming
involved in politics In this context the authors o Passage 1 are sug-
gesting that all members o society can have a ldquocommonrdquo or shared
happiness
Choices A C and D are incorrect because in this context ldquocommonrdquo does
not mean average coarse or similar
QUESTION 32
Choice C is the best answer In lines 25-30 the authors o Passage 1 state
that women should seek ldquogentle occupations and the cares o the homerdquo
so they can avoid perorming difficult or ldquostrenuousrdquo and unpleasant or
ldquoonerousrdquo tasks
Choices A B and D are incorrect because the authors o Passage 1 do notsuggest that running a household and raising children are rewarding or
both sexes yield less value or society or require proessional or political
skills
QUESTION 33
Choice C is the best answer In lines 25-30 the authors o Passage 1 provide
evidence that women should run households and raise children because
these roles do not require ldquostrenuous habits and onerous dutiesrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1040
9
Choices A B and D do not provide the best evidence that running a house-
hold and raising children entail very ew activities that are difficult or
unpleasant rather these lines offer general inormation about the differ-
ences between the sexes
QUESTION 34
Choice D is the best answer In lines 41-46 Wollstonecraf argues that i
women do not receive an education ldquoto become the companion o manrdquo or
one that is comparable to menrsquos education then society will not progress in
ldquoknowledge and virtuerdquo
Choices A B and C are incorrect because Wollstonecraf does not suggest
that society can progress only i women have happiness and financial secu-
rity ollow societal rules or replace men as figures o power
QUESTION 35
Choice C is the best answer Wollstonecraf argues that women should be
granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo
(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-
enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context
Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or
intellect and allow women to consider their role in society
Choices A B and D are incorrect because in this context ldquoreasonrdquo does not
mean motive sanity or explanation
QUESTION 36
Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws
passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to
ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf
is arguing that societyrsquos leaders grant men reedoms that are denied to women
Choices B C and D are incorrect because Wollstonecraf does not claim
that societyrsquos leaders have granted reedoms that created a general reduction
in individual virtue caused arguments about happiness or ensured equality
or all people
QUESTION 37
Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-
dence that societyrsquos leaders grant reedoms that privilege men She argues
that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-
lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to
ldquocontend or their reedomrdquo
Choices A B and C do not provide the best evidence that societyrsquos leaders
grant reedoms that privilege men over women
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1140
10
QUESTION 38
Choice C is the best answer Wollstonecraf cites the statement made by
the authors o Passage 1 that excluding women rom political participation
is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)
Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe
abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument
by highlighting a flaw in the reasoning presented by the authors o Passage 1
Choices A B and D are incorrect because Wollstonecraf does not reer to
the statement made in Passage 1 to call into question the authorsrsquo qualifica-
tions dispute the assertion that women are excluded by their own govern-
ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on
gender roles
QUESTION 39
Choice A is the best answer Te authors o Passage 1 argue that while
restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)
this restriction is necessary or societyrsquos overall happiness (lines 13-17)
Wollstonecraf however strongly challenges this argument asking the
authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-
doms are granted to women and likening societyrsquos male leaders to tyrants as
they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in
the darkrdquo (lines 78-88)
Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2
QUESTION 40
Choice D is the best answer Te authors o Passage 1 admit that women are
ldquoexcluded by the other hal [men] rom any participation in governmentrdquo
(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws
that deny women ldquocivil and political rightsrdquo (line 86)
Choices A B and C are incorrect because the authors o both passages
would not agree that women had the same preerences as men required agood education or were as happy as men
QUESTION 41
Choice A is the best answer Wollstonecraf argues in the final paragraph
o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women
ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would
most likely argue that allowing women these rights would be ldquoa reversal o
[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos
interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as
7262019 PrepScholar Sat Practice Test 3 Answers
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11
mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created
two sexes or a particular reason so while men can exercise civil and politi-
cal rights women are not naturally suited to these activities (lines 30-36)
Choices B and C are incorrect because they are not supported by inorma-
tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do
not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo
QUESTION 42
Choice C is the best answer When discussing problems with bee colo-
nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo
(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-
tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a
tentative tone and provides urther evidence that the authors believe but are
not certain that their hypothesis is correct
Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone
QUESTION 43
Choice C is the best answer In lines 24-28 the authors hypothesize that bee
colonies will be susceptible to mite inestations i they do not occasionally
eed on pyrethrum producing plants In lines 42-46 they suggest creating a
trial where a ldquosmall number o commercial honey bee colonies are offered a
number o pyrethrum producing plantsrdquo to test their hypothesis
Choices A B and D are incorrect because the authors do not hypothesize that
honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees
to develop secondary inections that beekeepers should increase their use o
insecticides or that humans are more susceptible to varroa mites
QUESTION 44
Choice D is the best answer In lines 24-28 the authors provide evidence
that a bee colony may be more resistant to mite inections i the bees eat
pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-
nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees
Choices A B and C do not describe any o the authorsrsquo hypotheses
QUESTION 45
Choice D is the best answer Te authors explain that when beekeepers
use commercially produced insecticides to fight mite inections they may
ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-
cientrdquo (lines 31-35)
7262019 PrepScholar Sat Practice Test 3 Answers
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12
Choices A B and C are incorrect because the authors do not suggest that
beekeepersrsquo use o commercially produced insecticides increases mite popu-
lations kills bacteria or destroys beesrsquo primary ood source
QUESTION 46
Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-
ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo
Choices A B and D are incorrect because they do not provide the best evi-
dence that beekeepersrsquo use o commercially produced insecticides may be
harmul to bees choices A B and D ocus on mite inestationsrsquo impact on
honeybees
QUESTION 47
Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some
bees Te authors then state ldquoWe urther postulate that the proper dosage
necessary to prevent mite inestation may be better lef to the beesrdquo (lines
35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the
bees may naturally control mite inestations better than insecticides
Choices A C and D are incorrect because in this context ldquopostulaterdquo does
not mean to make an unounded assumption question a belie or theory or
conclude based on firm evidence
QUESTION 48
Choice B is the best answer In the ourth paragraph the authors propose
a trial to study i honeybeesrsquo consumption o pyrethrum producing plants
helps the honeybees deend against mite inestations In the experiment the
authors plan to offer honey bee colonies both pyrethrum producing plants
and ldquoa typical bee ood source such as cloverrdquo to determine i these different
diets affect the beesrsquo susceptibility to mite inestations
Choices A C and D are incorrect because the main purpose o the ourth
paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished
experiment
QUESTION 49
Choice A is the best answer In lines 43-45 the authors propose a scien-
tific trial in which honeybees are ldquooffered a number o pyrethrum producing
plants as well as a typical bee ood source such as cloverrdquo Since the authors
contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood
sourcerdquo it can be assumed that clover does not produce pyrethrums
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13
Choice B is incorrect because it is stated in the passage Choices C and D are
incorrect because they are not assumptions made by the authors
QUESTION 50
Choice B is the best answer Te table shows that 77 percent o the honeybee
colonies with colony collapse disorder were inected by all our pathogens
Choices A C and D are incorrect because they do not identiy the percent
o honeybee colonies with colony collapse disorder that were inected by all
our pathogens as based on data in the table
QUESTION 51
Choice D is the best answer Te table shows that 81 percent o colo-
nies without colony collapse disorder were affected by the pathogen
Nosema ceranae
Choices A B and C are incorrect because they do not identiy the pathogen
that inected the highest percentage o honeybee colonies without colony
collapse disorder as based on data in the table
QUESTION 52
Choice D is the best answer Te table discusses pathogen occurrence in
honeybee colonies but it includes no inormation as to whether these hon-
eybees were inected with mites Because the table does not suggest mites
inested the honeybee colonies no conclusions can be made as to whether
mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)
Choices A B and C are incorrect because the table provides no inormation
about whether these honeybees were inected with mites
Section 2 Writing and Language Test
QUESTION 1
Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-
ates a parallel structure within the list that begins with ldquohappierrdquo
Choices B C and D are incorrect because none creates a parallel structure
within the list o qualities
QUESTION 2
Choice B is the best answer Te ways in which exposure to natural light
affects employees is the main subject o the passage
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14
Choices A C and D are incorrect because none introduces the topic dis-
cussed in the remainder o the passage
QUESTION 3
Choice C is the best answer It accurately notes that the proposed sentence
would be placed directly between the first mention o circadian rhythms andthe explanation o the term
Choices A B and D are incorrect because each misinterprets the relation-
ship between the proposed additional text and the ideas in the paragraph
QUESTION 4
Choice C is the best answer It provides the correct possessive construction
or ldquobodyrdquo which must be a singular noun when discussed in general terms
as in this sentence Choice C also provides the correct plural construction
or ldquoclocksrdquo
Choices A B and D are incorrect because each applies either a possessive or
a plural construction in a place where it doesnrsquot belong
QUESTION 5
Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular
noun ldquoabsenteeismrdquo
Choices B C and D are incorrect because each provides a verb that
either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy
QUESTION 6
Choice B is the best answer It contains a direct reerence to productivity
the topic introduced in the previous sentence
Choices A C and D are incorrect because none directly addresses employee
productivity the primary subject o the previous sentence
QUESTION 7
Choice A is the best answer It opens with a reerence to lowered worker
productivity creating a transition rom the previous paragraph and clearly
positions the high energy costs o artificial light sources as an additional
disadvantage
Choices B C and D are incorrect because none o the choices offer an ade-
quate transition rom the previous paragraph Each awkwardly inserts the
issue o lower worker productivity into a statement about the high energy
costs o artificial light sources
7262019 PrepScholar Sat Practice Test 3 Answers
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15
QUESTION 8
Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-
cate that the savings occurred every year
Choices A B and C are incorrect because each proposes an option that
would result in a redundancy with ldquoannualrdquo
QUESTION 9
Choice C is the best answer It provides a transitional adverb that accurately
communicates that this sentence describes an option that companies could
choose (ldquolight tubesrdquo) instead o the option described in the previous sen-
tence (ldquoull-pane windowsrdquo)
Choices A B and D are incorrect because each proposes a transitional
adverb that does not accurately reflect the relationship between this sen-
tence and the one preceding it
QUESTION 10
Choice C is the best answer It provides the correct relative pronoun to cor-
respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-
duce the definition that ollows
Choices A B and D are incorrect because each offers a pronoun inappropri-
ate or opening a dependent clause defining ldquolight tubesrdquo
QUESTION 11
Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the
noun ldquomeansrdquo particularly as a way to connect it to another noun or verb
Choices A C and D are incorrect because each results in nonstandard
phrasing with ldquomeansrdquo
QUESTION 12
Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-
responds with the plural noun ldquosettlersrdquo
Choices B C and D are incorrect because each provides either a nonstan-
dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo
QUESTION 13
Choice C is the best answer It creates a transition rom the poor ood qual-
ity mentioned in the previous sentence to the inormation about Harvey in
the remainder o the sentence
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16
Choices A B and D are incorrect because none offers a transition rom the
previous sentence or a detail that corresponds precisely with the inorma-
tion in the remainder o the sentence
QUESTION 14
Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens
with a comma
Choices A B and C are incorrect because each proposes punctuation that
creates an inappropriately strong separation between the subject ldquoFred
Harveyrdquo and the verb ldquodecidedrdquo
QUESTION 15
Choice B is the best answer It provides the plural verb and plural posses-
sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo
Choices A C and D are incorrect because each either ails to provide a verb
that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide
the appropriate possessive pronoun
QUESTION 16
Choice C is the best answer It accurately echoes an earlier characterization
o the ood as being o ldquoterrible qualityrdquo while maintaining the established
tone o the passage
Choices A B and D are incorrect either because the word is less ormal than
the established tone o the passage (ldquoickyrdquo) or because it illogically attributes
agency to ood (ldquosinisterrdquo ldquosurlyrdquo)
QUESTION 17
Choice C is the best answer It accurately interprets ldquonot content to ollow
conventional business practicesrdquo as logically introducing the new practice o
ldquoemploying womenrdquo described in the ollowing sentences
Choices A B and D are incorrect because none recognizes why the sentence
is relevant to this particular location in the passage
QUESTION 18
Choice B is the best answer It is concise and ree o redundancies
Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and
ldquotremendousrdquo adjectives so close in meaning that together they present a
redundancy
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17
QUESTION 19
Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary
reerence to ldquosuch regulationsrdquo in the previous clause
Choices A B and C are incorrect because each lacks a necessary subject
such as a pronoun or noun
QUESTION 20
Choice C is the best answer It reers directly to benefits or the restaurantsrsquo
emale employees the subject o the previous sentence
Choices A B and D are incorrect because none logically builds upon the
sentence that precedes it
QUESTION 21
Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo
Choices A B and C are incorrect because each uses the punctuation or
a dependent clause (ldquoLiving independently and demonstrating an intense
work ethicrdquo) as i it were an independent clause
QUESTION 22
Choice A is the best answer It recognizes that the new inormation sup-
ports the previous sentencersquos claim that ldquothe Harvey Girls became known as
a transormative orcerdquo
Choices B C and D are incorrect because each misinterprets the relation-
ship between the proposed text and the passage
QUESTION 23
Choice A is the best answer It opens with a clause that identifies how
1-MCP affects apples which ocuses the sentence on 1-MCP as the subject
and allows the ideas in the sentence to progress logically
Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy
QUESTION 24
Choice D is the best answer Only the comma is necessary to separate
ldquoethylenerdquo rom the appositive noun phrase that defines it
Choices A B and C are incorrect because each creates a comma splice and
or adds unnecessary words
7262019 PrepScholar Sat Practice Test 3 Answers
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18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
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19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
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22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
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24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
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25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
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28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740
36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3840
37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3940
38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040
QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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7
QUESTION 25
Choice C is the best answer When a rancher observed Dialrsquos laboratory
setup he was ldquoincredulousrdquo that the Chukars were living on the ground and
he advised Dial to give the birds ldquosomething to climb onrdquo (lines 16-23) Tis
ldquokey piece o advicerdquo (line 14) led Dial to add hay bales to his laboratory
Dial later noticed that the Chukars were using their legs and wings to scalethe hay bales and this observation became the ocal point o his research
Choices A B and D are incorrect because the incident with the local rancher
did not serve to reveal Dialrsquos motivation or creating the project emphasize
differences in laboratory and field research or introduce a contributor to a
scientific theory
QUESTION 26
Choice C is the best answer Te author explains that Dialrsquos ldquoaha momentrdquo
came when he determined the Chukars used ldquotheir legs and wings coop-erativelyrdquo to scale the hay bales (lines 40-42) Dial then created additional
experiments to study how the birds dealt with gradually steeper inclines
ldquo[he filmed] the birds as they raced up textured ramps tilted at increasing
anglesrdquo (lines 46-48)
Choices A B and D are incorrect because Dialrsquos ldquoaha momentrdquo was not ol-
lowed by Dial teaching the birds to fly studying videos to find out why the
birds no longer hopped or consulting with other researchers
QUESTION 27
Choice B is the best answer Dial observed that as the Chukars raced up
steep ramps they ldquobegan to flaprdquo and ldquoaimed their flapping down and back-
ward using the orce to keep their eet firmly pressed against the ramprdquo
(lines 49-53) Dial determined that the position o their flapping wings acil-
itated the baby Chukarsrsquo traction on the steep ramps
Choices A C and D are incorrect because the passage does not indicate that
the Chukarsrsquo speed alternation o wing and oot movement or continual
hopping motions acilitated their traction on steep ramps
QUESTION 28
Choice B is the best answer In lines 61-63 the author explains that Dial
named his scientific finding ldquoWAIR or wing-assisted incline running and
went on to document it in a wide range o speciesrdquo In this context Dial
ldquodocumentedrdquo or recorded the existence o WAIR in numerous bird species
Choices A C and D are incorrect because in this context ldquodocumentrdquo does
not mean to portray publish or process
7262019 PrepScholar Sat Practice Test 3 Answers
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8
QUESTION 29
Choice D is the best answer In lines 70-74 the author explains that glid-
ing animals do not use a ldquoflapping flight strokerdquo or WAIR wing-assisted
incline running Since Chukars a ground bird use WAIR to help scale steep
inclines it can be reasonably inerred that gliding animals do not use WAIR
to aid in climbing slopes
Choices A B and C are incorrect because the passage does not include
inormation on gliding animalsrsquo offspring their method o locomotion or
their eeding habits
QUESTION 30
Choice D is the best answer In lines 73-75 the author provides evidence
that ldquothe flapping flight strokerdquo is ldquosomething gliding animals donrsquot dordquo
Choices A B and C do not provide the best evidence that gliding animalsdo not use a flapping stroke to aid in climbing slopes Tese choices do not
contain inormation about gliding animals
QUESTION 31
Choice B is the best answer In lines 21-24 the authors o Passage 1 state
societyrsquos ldquocommon happinessrdquo is dependent on women never becoming
involved in politics In this context the authors o Passage 1 are sug-
gesting that all members o society can have a ldquocommonrdquo or shared
happiness
Choices A C and D are incorrect because in this context ldquocommonrdquo does
not mean average coarse or similar
QUESTION 32
Choice C is the best answer In lines 25-30 the authors o Passage 1 state
that women should seek ldquogentle occupations and the cares o the homerdquo
so they can avoid perorming difficult or ldquostrenuousrdquo and unpleasant or
ldquoonerousrdquo tasks
Choices A B and D are incorrect because the authors o Passage 1 do notsuggest that running a household and raising children are rewarding or
both sexes yield less value or society or require proessional or political
skills
QUESTION 33
Choice C is the best answer In lines 25-30 the authors o Passage 1 provide
evidence that women should run households and raise children because
these roles do not require ldquostrenuous habits and onerous dutiesrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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9
Choices A B and D do not provide the best evidence that running a house-
hold and raising children entail very ew activities that are difficult or
unpleasant rather these lines offer general inormation about the differ-
ences between the sexes
QUESTION 34
Choice D is the best answer In lines 41-46 Wollstonecraf argues that i
women do not receive an education ldquoto become the companion o manrdquo or
one that is comparable to menrsquos education then society will not progress in
ldquoknowledge and virtuerdquo
Choices A B and C are incorrect because Wollstonecraf does not suggest
that society can progress only i women have happiness and financial secu-
rity ollow societal rules or replace men as figures o power
QUESTION 35
Choice C is the best answer Wollstonecraf argues that women should be
granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo
(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-
enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context
Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or
intellect and allow women to consider their role in society
Choices A B and D are incorrect because in this context ldquoreasonrdquo does not
mean motive sanity or explanation
QUESTION 36
Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws
passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to
ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf
is arguing that societyrsquos leaders grant men reedoms that are denied to women
Choices B C and D are incorrect because Wollstonecraf does not claim
that societyrsquos leaders have granted reedoms that created a general reduction
in individual virtue caused arguments about happiness or ensured equality
or all people
QUESTION 37
Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-
dence that societyrsquos leaders grant reedoms that privilege men She argues
that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-
lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to
ldquocontend or their reedomrdquo
Choices A B and C do not provide the best evidence that societyrsquos leaders
grant reedoms that privilege men over women
7262019 PrepScholar Sat Practice Test 3 Answers
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10
QUESTION 38
Choice C is the best answer Wollstonecraf cites the statement made by
the authors o Passage 1 that excluding women rom political participation
is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)
Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe
abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument
by highlighting a flaw in the reasoning presented by the authors o Passage 1
Choices A B and D are incorrect because Wollstonecraf does not reer to
the statement made in Passage 1 to call into question the authorsrsquo qualifica-
tions dispute the assertion that women are excluded by their own govern-
ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on
gender roles
QUESTION 39
Choice A is the best answer Te authors o Passage 1 argue that while
restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)
this restriction is necessary or societyrsquos overall happiness (lines 13-17)
Wollstonecraf however strongly challenges this argument asking the
authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-
doms are granted to women and likening societyrsquos male leaders to tyrants as
they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in
the darkrdquo (lines 78-88)
Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2
QUESTION 40
Choice D is the best answer Te authors o Passage 1 admit that women are
ldquoexcluded by the other hal [men] rom any participation in governmentrdquo
(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws
that deny women ldquocivil and political rightsrdquo (line 86)
Choices A B and C are incorrect because the authors o both passages
would not agree that women had the same preerences as men required agood education or were as happy as men
QUESTION 41
Choice A is the best answer Wollstonecraf argues in the final paragraph
o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women
ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would
most likely argue that allowing women these rights would be ldquoa reversal o
[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos
interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as
7262019 PrepScholar Sat Practice Test 3 Answers
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11
mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created
two sexes or a particular reason so while men can exercise civil and politi-
cal rights women are not naturally suited to these activities (lines 30-36)
Choices B and C are incorrect because they are not supported by inorma-
tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do
not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo
QUESTION 42
Choice C is the best answer When discussing problems with bee colo-
nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo
(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-
tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a
tentative tone and provides urther evidence that the authors believe but are
not certain that their hypothesis is correct
Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone
QUESTION 43
Choice C is the best answer In lines 24-28 the authors hypothesize that bee
colonies will be susceptible to mite inestations i they do not occasionally
eed on pyrethrum producing plants In lines 42-46 they suggest creating a
trial where a ldquosmall number o commercial honey bee colonies are offered a
number o pyrethrum producing plantsrdquo to test their hypothesis
Choices A B and D are incorrect because the authors do not hypothesize that
honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees
to develop secondary inections that beekeepers should increase their use o
insecticides or that humans are more susceptible to varroa mites
QUESTION 44
Choice D is the best answer In lines 24-28 the authors provide evidence
that a bee colony may be more resistant to mite inections i the bees eat
pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-
nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees
Choices A B and C do not describe any o the authorsrsquo hypotheses
QUESTION 45
Choice D is the best answer Te authors explain that when beekeepers
use commercially produced insecticides to fight mite inections they may
ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-
cientrdquo (lines 31-35)
7262019 PrepScholar Sat Practice Test 3 Answers
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12
Choices A B and C are incorrect because the authors do not suggest that
beekeepersrsquo use o commercially produced insecticides increases mite popu-
lations kills bacteria or destroys beesrsquo primary ood source
QUESTION 46
Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-
ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo
Choices A B and D are incorrect because they do not provide the best evi-
dence that beekeepersrsquo use o commercially produced insecticides may be
harmul to bees choices A B and D ocus on mite inestationsrsquo impact on
honeybees
QUESTION 47
Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some
bees Te authors then state ldquoWe urther postulate that the proper dosage
necessary to prevent mite inestation may be better lef to the beesrdquo (lines
35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the
bees may naturally control mite inestations better than insecticides
Choices A C and D are incorrect because in this context ldquopostulaterdquo does
not mean to make an unounded assumption question a belie or theory or
conclude based on firm evidence
QUESTION 48
Choice B is the best answer In the ourth paragraph the authors propose
a trial to study i honeybeesrsquo consumption o pyrethrum producing plants
helps the honeybees deend against mite inestations In the experiment the
authors plan to offer honey bee colonies both pyrethrum producing plants
and ldquoa typical bee ood source such as cloverrdquo to determine i these different
diets affect the beesrsquo susceptibility to mite inestations
Choices A C and D are incorrect because the main purpose o the ourth
paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished
experiment
QUESTION 49
Choice A is the best answer In lines 43-45 the authors propose a scien-
tific trial in which honeybees are ldquooffered a number o pyrethrum producing
plants as well as a typical bee ood source such as cloverrdquo Since the authors
contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood
sourcerdquo it can be assumed that clover does not produce pyrethrums
7262019 PrepScholar Sat Practice Test 3 Answers
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13
Choice B is incorrect because it is stated in the passage Choices C and D are
incorrect because they are not assumptions made by the authors
QUESTION 50
Choice B is the best answer Te table shows that 77 percent o the honeybee
colonies with colony collapse disorder were inected by all our pathogens
Choices A C and D are incorrect because they do not identiy the percent
o honeybee colonies with colony collapse disorder that were inected by all
our pathogens as based on data in the table
QUESTION 51
Choice D is the best answer Te table shows that 81 percent o colo-
nies without colony collapse disorder were affected by the pathogen
Nosema ceranae
Choices A B and C are incorrect because they do not identiy the pathogen
that inected the highest percentage o honeybee colonies without colony
collapse disorder as based on data in the table
QUESTION 52
Choice D is the best answer Te table discusses pathogen occurrence in
honeybee colonies but it includes no inormation as to whether these hon-
eybees were inected with mites Because the table does not suggest mites
inested the honeybee colonies no conclusions can be made as to whether
mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)
Choices A B and C are incorrect because the table provides no inormation
about whether these honeybees were inected with mites
Section 2 Writing and Language Test
QUESTION 1
Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-
ates a parallel structure within the list that begins with ldquohappierrdquo
Choices B C and D are incorrect because none creates a parallel structure
within the list o qualities
QUESTION 2
Choice B is the best answer Te ways in which exposure to natural light
affects employees is the main subject o the passage
7262019 PrepScholar Sat Practice Test 3 Answers
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14
Choices A C and D are incorrect because none introduces the topic dis-
cussed in the remainder o the passage
QUESTION 3
Choice C is the best answer It accurately notes that the proposed sentence
would be placed directly between the first mention o circadian rhythms andthe explanation o the term
Choices A B and D are incorrect because each misinterprets the relation-
ship between the proposed additional text and the ideas in the paragraph
QUESTION 4
Choice C is the best answer It provides the correct possessive construction
or ldquobodyrdquo which must be a singular noun when discussed in general terms
as in this sentence Choice C also provides the correct plural construction
or ldquoclocksrdquo
Choices A B and D are incorrect because each applies either a possessive or
a plural construction in a place where it doesnrsquot belong
QUESTION 5
Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular
noun ldquoabsenteeismrdquo
Choices B C and D are incorrect because each provides a verb that
either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy
QUESTION 6
Choice B is the best answer It contains a direct reerence to productivity
the topic introduced in the previous sentence
Choices A C and D are incorrect because none directly addresses employee
productivity the primary subject o the previous sentence
QUESTION 7
Choice A is the best answer It opens with a reerence to lowered worker
productivity creating a transition rom the previous paragraph and clearly
positions the high energy costs o artificial light sources as an additional
disadvantage
Choices B C and D are incorrect because none o the choices offer an ade-
quate transition rom the previous paragraph Each awkwardly inserts the
issue o lower worker productivity into a statement about the high energy
costs o artificial light sources
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1640
15
QUESTION 8
Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-
cate that the savings occurred every year
Choices A B and C are incorrect because each proposes an option that
would result in a redundancy with ldquoannualrdquo
QUESTION 9
Choice C is the best answer It provides a transitional adverb that accurately
communicates that this sentence describes an option that companies could
choose (ldquolight tubesrdquo) instead o the option described in the previous sen-
tence (ldquoull-pane windowsrdquo)
Choices A B and D are incorrect because each proposes a transitional
adverb that does not accurately reflect the relationship between this sen-
tence and the one preceding it
QUESTION 10
Choice C is the best answer It provides the correct relative pronoun to cor-
respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-
duce the definition that ollows
Choices A B and D are incorrect because each offers a pronoun inappropri-
ate or opening a dependent clause defining ldquolight tubesrdquo
QUESTION 11
Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the
noun ldquomeansrdquo particularly as a way to connect it to another noun or verb
Choices A C and D are incorrect because each results in nonstandard
phrasing with ldquomeansrdquo
QUESTION 12
Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-
responds with the plural noun ldquosettlersrdquo
Choices B C and D are incorrect because each provides either a nonstan-
dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo
QUESTION 13
Choice C is the best answer It creates a transition rom the poor ood qual-
ity mentioned in the previous sentence to the inormation about Harvey in
the remainder o the sentence
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1740
16
Choices A B and D are incorrect because none offers a transition rom the
previous sentence or a detail that corresponds precisely with the inorma-
tion in the remainder o the sentence
QUESTION 14
Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens
with a comma
Choices A B and C are incorrect because each proposes punctuation that
creates an inappropriately strong separation between the subject ldquoFred
Harveyrdquo and the verb ldquodecidedrdquo
QUESTION 15
Choice B is the best answer It provides the plural verb and plural posses-
sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo
Choices A C and D are incorrect because each either ails to provide a verb
that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide
the appropriate possessive pronoun
QUESTION 16
Choice C is the best answer It accurately echoes an earlier characterization
o the ood as being o ldquoterrible qualityrdquo while maintaining the established
tone o the passage
Choices A B and D are incorrect either because the word is less ormal than
the established tone o the passage (ldquoickyrdquo) or because it illogically attributes
agency to ood (ldquosinisterrdquo ldquosurlyrdquo)
QUESTION 17
Choice C is the best answer It accurately interprets ldquonot content to ollow
conventional business practicesrdquo as logically introducing the new practice o
ldquoemploying womenrdquo described in the ollowing sentences
Choices A B and D are incorrect because none recognizes why the sentence
is relevant to this particular location in the passage
QUESTION 18
Choice B is the best answer It is concise and ree o redundancies
Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and
ldquotremendousrdquo adjectives so close in meaning that together they present a
redundancy
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840
17
QUESTION 19
Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary
reerence to ldquosuch regulationsrdquo in the previous clause
Choices A B and C are incorrect because each lacks a necessary subject
such as a pronoun or noun
QUESTION 20
Choice C is the best answer It reers directly to benefits or the restaurantsrsquo
emale employees the subject o the previous sentence
Choices A B and D are incorrect because none logically builds upon the
sentence that precedes it
QUESTION 21
Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo
Choices A B and C are incorrect because each uses the punctuation or
a dependent clause (ldquoLiving independently and demonstrating an intense
work ethicrdquo) as i it were an independent clause
QUESTION 22
Choice A is the best answer It recognizes that the new inormation sup-
ports the previous sentencersquos claim that ldquothe Harvey Girls became known as
a transormative orcerdquo
Choices B C and D are incorrect because each misinterprets the relation-
ship between the proposed text and the passage
QUESTION 23
Choice A is the best answer It opens with a clause that identifies how
1-MCP affects apples which ocuses the sentence on 1-MCP as the subject
and allows the ideas in the sentence to progress logically
Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy
QUESTION 24
Choice D is the best answer Only the comma is necessary to separate
ldquoethylenerdquo rom the appositive noun phrase that defines it
Choices A B and C are incorrect because each creates a comma splice and
or adds unnecessary words
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1940
18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040
19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140
20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240
21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340
22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440
23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640
25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940
28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040
29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640
35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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8
QUESTION 29
Choice D is the best answer In lines 70-74 the author explains that glid-
ing animals do not use a ldquoflapping flight strokerdquo or WAIR wing-assisted
incline running Since Chukars a ground bird use WAIR to help scale steep
inclines it can be reasonably inerred that gliding animals do not use WAIR
to aid in climbing slopes
Choices A B and C are incorrect because the passage does not include
inormation on gliding animalsrsquo offspring their method o locomotion or
their eeding habits
QUESTION 30
Choice D is the best answer In lines 73-75 the author provides evidence
that ldquothe flapping flight strokerdquo is ldquosomething gliding animals donrsquot dordquo
Choices A B and C do not provide the best evidence that gliding animalsdo not use a flapping stroke to aid in climbing slopes Tese choices do not
contain inormation about gliding animals
QUESTION 31
Choice B is the best answer In lines 21-24 the authors o Passage 1 state
societyrsquos ldquocommon happinessrdquo is dependent on women never becoming
involved in politics In this context the authors o Passage 1 are sug-
gesting that all members o society can have a ldquocommonrdquo or shared
happiness
Choices A C and D are incorrect because in this context ldquocommonrdquo does
not mean average coarse or similar
QUESTION 32
Choice C is the best answer In lines 25-30 the authors o Passage 1 state
that women should seek ldquogentle occupations and the cares o the homerdquo
so they can avoid perorming difficult or ldquostrenuousrdquo and unpleasant or
ldquoonerousrdquo tasks
Choices A B and D are incorrect because the authors o Passage 1 do notsuggest that running a household and raising children are rewarding or
both sexes yield less value or society or require proessional or political
skills
QUESTION 33
Choice C is the best answer In lines 25-30 the authors o Passage 1 provide
evidence that women should run households and raise children because
these roles do not require ldquostrenuous habits and onerous dutiesrdquo
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9
Choices A B and D do not provide the best evidence that running a house-
hold and raising children entail very ew activities that are difficult or
unpleasant rather these lines offer general inormation about the differ-
ences between the sexes
QUESTION 34
Choice D is the best answer In lines 41-46 Wollstonecraf argues that i
women do not receive an education ldquoto become the companion o manrdquo or
one that is comparable to menrsquos education then society will not progress in
ldquoknowledge and virtuerdquo
Choices A B and C are incorrect because Wollstonecraf does not suggest
that society can progress only i women have happiness and financial secu-
rity ollow societal rules or replace men as figures o power
QUESTION 35
Choice C is the best answer Wollstonecraf argues that women should be
granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo
(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-
enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context
Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or
intellect and allow women to consider their role in society
Choices A B and D are incorrect because in this context ldquoreasonrdquo does not
mean motive sanity or explanation
QUESTION 36
Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws
passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to
ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf
is arguing that societyrsquos leaders grant men reedoms that are denied to women
Choices B C and D are incorrect because Wollstonecraf does not claim
that societyrsquos leaders have granted reedoms that created a general reduction
in individual virtue caused arguments about happiness or ensured equality
or all people
QUESTION 37
Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-
dence that societyrsquos leaders grant reedoms that privilege men She argues
that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-
lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to
ldquocontend or their reedomrdquo
Choices A B and C do not provide the best evidence that societyrsquos leaders
grant reedoms that privilege men over women
7262019 PrepScholar Sat Practice Test 3 Answers
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10
QUESTION 38
Choice C is the best answer Wollstonecraf cites the statement made by
the authors o Passage 1 that excluding women rom political participation
is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)
Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe
abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument
by highlighting a flaw in the reasoning presented by the authors o Passage 1
Choices A B and D are incorrect because Wollstonecraf does not reer to
the statement made in Passage 1 to call into question the authorsrsquo qualifica-
tions dispute the assertion that women are excluded by their own govern-
ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on
gender roles
QUESTION 39
Choice A is the best answer Te authors o Passage 1 argue that while
restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)
this restriction is necessary or societyrsquos overall happiness (lines 13-17)
Wollstonecraf however strongly challenges this argument asking the
authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-
doms are granted to women and likening societyrsquos male leaders to tyrants as
they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in
the darkrdquo (lines 78-88)
Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2
QUESTION 40
Choice D is the best answer Te authors o Passage 1 admit that women are
ldquoexcluded by the other hal [men] rom any participation in governmentrdquo
(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws
that deny women ldquocivil and political rightsrdquo (line 86)
Choices A B and C are incorrect because the authors o both passages
would not agree that women had the same preerences as men required agood education or were as happy as men
QUESTION 41
Choice A is the best answer Wollstonecraf argues in the final paragraph
o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women
ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would
most likely argue that allowing women these rights would be ldquoa reversal o
[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos
interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as
7262019 PrepScholar Sat Practice Test 3 Answers
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11
mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created
two sexes or a particular reason so while men can exercise civil and politi-
cal rights women are not naturally suited to these activities (lines 30-36)
Choices B and C are incorrect because they are not supported by inorma-
tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do
not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo
QUESTION 42
Choice C is the best answer When discussing problems with bee colo-
nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo
(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-
tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a
tentative tone and provides urther evidence that the authors believe but are
not certain that their hypothesis is correct
Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone
QUESTION 43
Choice C is the best answer In lines 24-28 the authors hypothesize that bee
colonies will be susceptible to mite inestations i they do not occasionally
eed on pyrethrum producing plants In lines 42-46 they suggest creating a
trial where a ldquosmall number o commercial honey bee colonies are offered a
number o pyrethrum producing plantsrdquo to test their hypothesis
Choices A B and D are incorrect because the authors do not hypothesize that
honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees
to develop secondary inections that beekeepers should increase their use o
insecticides or that humans are more susceptible to varroa mites
QUESTION 44
Choice D is the best answer In lines 24-28 the authors provide evidence
that a bee colony may be more resistant to mite inections i the bees eat
pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-
nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees
Choices A B and C do not describe any o the authorsrsquo hypotheses
QUESTION 45
Choice D is the best answer Te authors explain that when beekeepers
use commercially produced insecticides to fight mite inections they may
ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-
cientrdquo (lines 31-35)
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12
Choices A B and C are incorrect because the authors do not suggest that
beekeepersrsquo use o commercially produced insecticides increases mite popu-
lations kills bacteria or destroys beesrsquo primary ood source
QUESTION 46
Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-
ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo
Choices A B and D are incorrect because they do not provide the best evi-
dence that beekeepersrsquo use o commercially produced insecticides may be
harmul to bees choices A B and D ocus on mite inestationsrsquo impact on
honeybees
QUESTION 47
Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some
bees Te authors then state ldquoWe urther postulate that the proper dosage
necessary to prevent mite inestation may be better lef to the beesrdquo (lines
35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the
bees may naturally control mite inestations better than insecticides
Choices A C and D are incorrect because in this context ldquopostulaterdquo does
not mean to make an unounded assumption question a belie or theory or
conclude based on firm evidence
QUESTION 48
Choice B is the best answer In the ourth paragraph the authors propose
a trial to study i honeybeesrsquo consumption o pyrethrum producing plants
helps the honeybees deend against mite inestations In the experiment the
authors plan to offer honey bee colonies both pyrethrum producing plants
and ldquoa typical bee ood source such as cloverrdquo to determine i these different
diets affect the beesrsquo susceptibility to mite inestations
Choices A C and D are incorrect because the main purpose o the ourth
paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished
experiment
QUESTION 49
Choice A is the best answer In lines 43-45 the authors propose a scien-
tific trial in which honeybees are ldquooffered a number o pyrethrum producing
plants as well as a typical bee ood source such as cloverrdquo Since the authors
contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood
sourcerdquo it can be assumed that clover does not produce pyrethrums
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13
Choice B is incorrect because it is stated in the passage Choices C and D are
incorrect because they are not assumptions made by the authors
QUESTION 50
Choice B is the best answer Te table shows that 77 percent o the honeybee
colonies with colony collapse disorder were inected by all our pathogens
Choices A C and D are incorrect because they do not identiy the percent
o honeybee colonies with colony collapse disorder that were inected by all
our pathogens as based on data in the table
QUESTION 51
Choice D is the best answer Te table shows that 81 percent o colo-
nies without colony collapse disorder were affected by the pathogen
Nosema ceranae
Choices A B and C are incorrect because they do not identiy the pathogen
that inected the highest percentage o honeybee colonies without colony
collapse disorder as based on data in the table
QUESTION 52
Choice D is the best answer Te table discusses pathogen occurrence in
honeybee colonies but it includes no inormation as to whether these hon-
eybees were inected with mites Because the table does not suggest mites
inested the honeybee colonies no conclusions can be made as to whether
mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)
Choices A B and C are incorrect because the table provides no inormation
about whether these honeybees were inected with mites
Section 2 Writing and Language Test
QUESTION 1
Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-
ates a parallel structure within the list that begins with ldquohappierrdquo
Choices B C and D are incorrect because none creates a parallel structure
within the list o qualities
QUESTION 2
Choice B is the best answer Te ways in which exposure to natural light
affects employees is the main subject o the passage
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14
Choices A C and D are incorrect because none introduces the topic dis-
cussed in the remainder o the passage
QUESTION 3
Choice C is the best answer It accurately notes that the proposed sentence
would be placed directly between the first mention o circadian rhythms andthe explanation o the term
Choices A B and D are incorrect because each misinterprets the relation-
ship between the proposed additional text and the ideas in the paragraph
QUESTION 4
Choice C is the best answer It provides the correct possessive construction
or ldquobodyrdquo which must be a singular noun when discussed in general terms
as in this sentence Choice C also provides the correct plural construction
or ldquoclocksrdquo
Choices A B and D are incorrect because each applies either a possessive or
a plural construction in a place where it doesnrsquot belong
QUESTION 5
Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular
noun ldquoabsenteeismrdquo
Choices B C and D are incorrect because each provides a verb that
either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy
QUESTION 6
Choice B is the best answer It contains a direct reerence to productivity
the topic introduced in the previous sentence
Choices A C and D are incorrect because none directly addresses employee
productivity the primary subject o the previous sentence
QUESTION 7
Choice A is the best answer It opens with a reerence to lowered worker
productivity creating a transition rom the previous paragraph and clearly
positions the high energy costs o artificial light sources as an additional
disadvantage
Choices B C and D are incorrect because none o the choices offer an ade-
quate transition rom the previous paragraph Each awkwardly inserts the
issue o lower worker productivity into a statement about the high energy
costs o artificial light sources
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15
QUESTION 8
Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-
cate that the savings occurred every year
Choices A B and C are incorrect because each proposes an option that
would result in a redundancy with ldquoannualrdquo
QUESTION 9
Choice C is the best answer It provides a transitional adverb that accurately
communicates that this sentence describes an option that companies could
choose (ldquolight tubesrdquo) instead o the option described in the previous sen-
tence (ldquoull-pane windowsrdquo)
Choices A B and D are incorrect because each proposes a transitional
adverb that does not accurately reflect the relationship between this sen-
tence and the one preceding it
QUESTION 10
Choice C is the best answer It provides the correct relative pronoun to cor-
respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-
duce the definition that ollows
Choices A B and D are incorrect because each offers a pronoun inappropri-
ate or opening a dependent clause defining ldquolight tubesrdquo
QUESTION 11
Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the
noun ldquomeansrdquo particularly as a way to connect it to another noun or verb
Choices A C and D are incorrect because each results in nonstandard
phrasing with ldquomeansrdquo
QUESTION 12
Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-
responds with the plural noun ldquosettlersrdquo
Choices B C and D are incorrect because each provides either a nonstan-
dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo
QUESTION 13
Choice C is the best answer It creates a transition rom the poor ood qual-
ity mentioned in the previous sentence to the inormation about Harvey in
the remainder o the sentence
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16
Choices A B and D are incorrect because none offers a transition rom the
previous sentence or a detail that corresponds precisely with the inorma-
tion in the remainder o the sentence
QUESTION 14
Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens
with a comma
Choices A B and C are incorrect because each proposes punctuation that
creates an inappropriately strong separation between the subject ldquoFred
Harveyrdquo and the verb ldquodecidedrdquo
QUESTION 15
Choice B is the best answer It provides the plural verb and plural posses-
sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo
Choices A C and D are incorrect because each either ails to provide a verb
that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide
the appropriate possessive pronoun
QUESTION 16
Choice C is the best answer It accurately echoes an earlier characterization
o the ood as being o ldquoterrible qualityrdquo while maintaining the established
tone o the passage
Choices A B and D are incorrect either because the word is less ormal than
the established tone o the passage (ldquoickyrdquo) or because it illogically attributes
agency to ood (ldquosinisterrdquo ldquosurlyrdquo)
QUESTION 17
Choice C is the best answer It accurately interprets ldquonot content to ollow
conventional business practicesrdquo as logically introducing the new practice o
ldquoemploying womenrdquo described in the ollowing sentences
Choices A B and D are incorrect because none recognizes why the sentence
is relevant to this particular location in the passage
QUESTION 18
Choice B is the best answer It is concise and ree o redundancies
Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and
ldquotremendousrdquo adjectives so close in meaning that together they present a
redundancy
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17
QUESTION 19
Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary
reerence to ldquosuch regulationsrdquo in the previous clause
Choices A B and C are incorrect because each lacks a necessary subject
such as a pronoun or noun
QUESTION 20
Choice C is the best answer It reers directly to benefits or the restaurantsrsquo
emale employees the subject o the previous sentence
Choices A B and D are incorrect because none logically builds upon the
sentence that precedes it
QUESTION 21
Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo
Choices A B and C are incorrect because each uses the punctuation or
a dependent clause (ldquoLiving independently and demonstrating an intense
work ethicrdquo) as i it were an independent clause
QUESTION 22
Choice A is the best answer It recognizes that the new inormation sup-
ports the previous sentencersquos claim that ldquothe Harvey Girls became known as
a transormative orcerdquo
Choices B C and D are incorrect because each misinterprets the relation-
ship between the proposed text and the passage
QUESTION 23
Choice A is the best answer It opens with a clause that identifies how
1-MCP affects apples which ocuses the sentence on 1-MCP as the subject
and allows the ideas in the sentence to progress logically
Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy
QUESTION 24
Choice D is the best answer Only the comma is necessary to separate
ldquoethylenerdquo rom the appositive noun phrase that defines it
Choices A B and C are incorrect because each creates a comma splice and
or adds unnecessary words
7262019 PrepScholar Sat Practice Test 3 Answers
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18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
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19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
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22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440
23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640
25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
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27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
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28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3540
34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640
35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740
36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3840
37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3940
38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040
QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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9
Choices A B and D do not provide the best evidence that running a house-
hold and raising children entail very ew activities that are difficult or
unpleasant rather these lines offer general inormation about the differ-
ences between the sexes
QUESTION 34
Choice D is the best answer In lines 41-46 Wollstonecraf argues that i
women do not receive an education ldquoto become the companion o manrdquo or
one that is comparable to menrsquos education then society will not progress in
ldquoknowledge and virtuerdquo
Choices A B and C are incorrect because Wollstonecraf does not suggest
that society can progress only i women have happiness and financial secu-
rity ollow societal rules or replace men as figures o power
QUESTION 35
Choice C is the best answer Wollstonecraf argues that women should be
granted an education comparable to menrsquos so that truth is ldquocommon to allrdquo
(lines 41-46) Wollstonecraf states that education will ldquostrengthen [wom-
enrsquos] reason till she comprehend her dutyrdquo (lines 49-50) In this context
Wollstonecraf is arguing that education will improve womenrsquos ldquoreasonrdquo or
intellect and allow women to consider their role in society
Choices A B and D are incorrect because in this context ldquoreasonrdquo does not
mean motive sanity or explanation
QUESTION 36
Choice A is the best answer In lines 72-78 Wollstonecraf argues that the laws
passed by societyrsquos leaders allow men to ldquocontend or their reedomrdquo but serve to
ldquosubjugate womenrdquo In this context ldquosubjugaterdquo means to control Wollstonecraf
is arguing that societyrsquos leaders grant men reedoms that are denied to women
Choices B C and D are incorrect because Wollstonecraf does not claim
that societyrsquos leaders have granted reedoms that created a general reduction
in individual virtue caused arguments about happiness or ensured equality
or all people
QUESTION 37
Choice D is the best answer In lines 72-75 Wollstonecraf provides evi-
dence that societyrsquos leaders grant reedoms that privilege men She argues
that while societyrsquos leaders believe they ldquoare acting in the manner best calcu-
lated to promote [womenrsquos] happinessrdquo their decisions donrsquot allow women to
ldquocontend or their reedomrdquo
Choices A B and C do not provide the best evidence that societyrsquos leaders
grant reedoms that privilege men over women
7262019 PrepScholar Sat Practice Test 3 Answers
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10
QUESTION 38
Choice C is the best answer Wollstonecraf cites the statement made by
the authors o Passage 1 that excluding women rom political participation
is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)
Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe
abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument
by highlighting a flaw in the reasoning presented by the authors o Passage 1
Choices A B and D are incorrect because Wollstonecraf does not reer to
the statement made in Passage 1 to call into question the authorsrsquo qualifica-
tions dispute the assertion that women are excluded by their own govern-
ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on
gender roles
QUESTION 39
Choice A is the best answer Te authors o Passage 1 argue that while
restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)
this restriction is necessary or societyrsquos overall happiness (lines 13-17)
Wollstonecraf however strongly challenges this argument asking the
authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-
doms are granted to women and likening societyrsquos male leaders to tyrants as
they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in
the darkrdquo (lines 78-88)
Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2
QUESTION 40
Choice D is the best answer Te authors o Passage 1 admit that women are
ldquoexcluded by the other hal [men] rom any participation in governmentrdquo
(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws
that deny women ldquocivil and political rightsrdquo (line 86)
Choices A B and C are incorrect because the authors o both passages
would not agree that women had the same preerences as men required agood education or were as happy as men
QUESTION 41
Choice A is the best answer Wollstonecraf argues in the final paragraph
o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women
ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would
most likely argue that allowing women these rights would be ldquoa reversal o
[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos
interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as
7262019 PrepScholar Sat Practice Test 3 Answers
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11
mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created
two sexes or a particular reason so while men can exercise civil and politi-
cal rights women are not naturally suited to these activities (lines 30-36)
Choices B and C are incorrect because they are not supported by inorma-
tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do
not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo
QUESTION 42
Choice C is the best answer When discussing problems with bee colo-
nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo
(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-
tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a
tentative tone and provides urther evidence that the authors believe but are
not certain that their hypothesis is correct
Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone
QUESTION 43
Choice C is the best answer In lines 24-28 the authors hypothesize that bee
colonies will be susceptible to mite inestations i they do not occasionally
eed on pyrethrum producing plants In lines 42-46 they suggest creating a
trial where a ldquosmall number o commercial honey bee colonies are offered a
number o pyrethrum producing plantsrdquo to test their hypothesis
Choices A B and D are incorrect because the authors do not hypothesize that
honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees
to develop secondary inections that beekeepers should increase their use o
insecticides or that humans are more susceptible to varroa mites
QUESTION 44
Choice D is the best answer In lines 24-28 the authors provide evidence
that a bee colony may be more resistant to mite inections i the bees eat
pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-
nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees
Choices A B and C do not describe any o the authorsrsquo hypotheses
QUESTION 45
Choice D is the best answer Te authors explain that when beekeepers
use commercially produced insecticides to fight mite inections they may
ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-
cientrdquo (lines 31-35)
7262019 PrepScholar Sat Practice Test 3 Answers
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12
Choices A B and C are incorrect because the authors do not suggest that
beekeepersrsquo use o commercially produced insecticides increases mite popu-
lations kills bacteria or destroys beesrsquo primary ood source
QUESTION 46
Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-
ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo
Choices A B and D are incorrect because they do not provide the best evi-
dence that beekeepersrsquo use o commercially produced insecticides may be
harmul to bees choices A B and D ocus on mite inestationsrsquo impact on
honeybees
QUESTION 47
Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some
bees Te authors then state ldquoWe urther postulate that the proper dosage
necessary to prevent mite inestation may be better lef to the beesrdquo (lines
35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the
bees may naturally control mite inestations better than insecticides
Choices A C and D are incorrect because in this context ldquopostulaterdquo does
not mean to make an unounded assumption question a belie or theory or
conclude based on firm evidence
QUESTION 48
Choice B is the best answer In the ourth paragraph the authors propose
a trial to study i honeybeesrsquo consumption o pyrethrum producing plants
helps the honeybees deend against mite inestations In the experiment the
authors plan to offer honey bee colonies both pyrethrum producing plants
and ldquoa typical bee ood source such as cloverrdquo to determine i these different
diets affect the beesrsquo susceptibility to mite inestations
Choices A C and D are incorrect because the main purpose o the ourth
paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished
experiment
QUESTION 49
Choice A is the best answer In lines 43-45 the authors propose a scien-
tific trial in which honeybees are ldquooffered a number o pyrethrum producing
plants as well as a typical bee ood source such as cloverrdquo Since the authors
contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood
sourcerdquo it can be assumed that clover does not produce pyrethrums
7262019 PrepScholar Sat Practice Test 3 Answers
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13
Choice B is incorrect because it is stated in the passage Choices C and D are
incorrect because they are not assumptions made by the authors
QUESTION 50
Choice B is the best answer Te table shows that 77 percent o the honeybee
colonies with colony collapse disorder were inected by all our pathogens
Choices A C and D are incorrect because they do not identiy the percent
o honeybee colonies with colony collapse disorder that were inected by all
our pathogens as based on data in the table
QUESTION 51
Choice D is the best answer Te table shows that 81 percent o colo-
nies without colony collapse disorder were affected by the pathogen
Nosema ceranae
Choices A B and C are incorrect because they do not identiy the pathogen
that inected the highest percentage o honeybee colonies without colony
collapse disorder as based on data in the table
QUESTION 52
Choice D is the best answer Te table discusses pathogen occurrence in
honeybee colonies but it includes no inormation as to whether these hon-
eybees were inected with mites Because the table does not suggest mites
inested the honeybee colonies no conclusions can be made as to whether
mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)
Choices A B and C are incorrect because the table provides no inormation
about whether these honeybees were inected with mites
Section 2 Writing and Language Test
QUESTION 1
Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-
ates a parallel structure within the list that begins with ldquohappierrdquo
Choices B C and D are incorrect because none creates a parallel structure
within the list o qualities
QUESTION 2
Choice B is the best answer Te ways in which exposure to natural light
affects employees is the main subject o the passage
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1540
14
Choices A C and D are incorrect because none introduces the topic dis-
cussed in the remainder o the passage
QUESTION 3
Choice C is the best answer It accurately notes that the proposed sentence
would be placed directly between the first mention o circadian rhythms andthe explanation o the term
Choices A B and D are incorrect because each misinterprets the relation-
ship between the proposed additional text and the ideas in the paragraph
QUESTION 4
Choice C is the best answer It provides the correct possessive construction
or ldquobodyrdquo which must be a singular noun when discussed in general terms
as in this sentence Choice C also provides the correct plural construction
or ldquoclocksrdquo
Choices A B and D are incorrect because each applies either a possessive or
a plural construction in a place where it doesnrsquot belong
QUESTION 5
Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular
noun ldquoabsenteeismrdquo
Choices B C and D are incorrect because each provides a verb that
either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy
QUESTION 6
Choice B is the best answer It contains a direct reerence to productivity
the topic introduced in the previous sentence
Choices A C and D are incorrect because none directly addresses employee
productivity the primary subject o the previous sentence
QUESTION 7
Choice A is the best answer It opens with a reerence to lowered worker
productivity creating a transition rom the previous paragraph and clearly
positions the high energy costs o artificial light sources as an additional
disadvantage
Choices B C and D are incorrect because none o the choices offer an ade-
quate transition rom the previous paragraph Each awkwardly inserts the
issue o lower worker productivity into a statement about the high energy
costs o artificial light sources
7262019 PrepScholar Sat Practice Test 3 Answers
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15
QUESTION 8
Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-
cate that the savings occurred every year
Choices A B and C are incorrect because each proposes an option that
would result in a redundancy with ldquoannualrdquo
QUESTION 9
Choice C is the best answer It provides a transitional adverb that accurately
communicates that this sentence describes an option that companies could
choose (ldquolight tubesrdquo) instead o the option described in the previous sen-
tence (ldquoull-pane windowsrdquo)
Choices A B and D are incorrect because each proposes a transitional
adverb that does not accurately reflect the relationship between this sen-
tence and the one preceding it
QUESTION 10
Choice C is the best answer It provides the correct relative pronoun to cor-
respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-
duce the definition that ollows
Choices A B and D are incorrect because each offers a pronoun inappropri-
ate or opening a dependent clause defining ldquolight tubesrdquo
QUESTION 11
Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the
noun ldquomeansrdquo particularly as a way to connect it to another noun or verb
Choices A C and D are incorrect because each results in nonstandard
phrasing with ldquomeansrdquo
QUESTION 12
Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-
responds with the plural noun ldquosettlersrdquo
Choices B C and D are incorrect because each provides either a nonstan-
dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo
QUESTION 13
Choice C is the best answer It creates a transition rom the poor ood qual-
ity mentioned in the previous sentence to the inormation about Harvey in
the remainder o the sentence
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1740
16
Choices A B and D are incorrect because none offers a transition rom the
previous sentence or a detail that corresponds precisely with the inorma-
tion in the remainder o the sentence
QUESTION 14
Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens
with a comma
Choices A B and C are incorrect because each proposes punctuation that
creates an inappropriately strong separation between the subject ldquoFred
Harveyrdquo and the verb ldquodecidedrdquo
QUESTION 15
Choice B is the best answer It provides the plural verb and plural posses-
sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo
Choices A C and D are incorrect because each either ails to provide a verb
that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide
the appropriate possessive pronoun
QUESTION 16
Choice C is the best answer It accurately echoes an earlier characterization
o the ood as being o ldquoterrible qualityrdquo while maintaining the established
tone o the passage
Choices A B and D are incorrect either because the word is less ormal than
the established tone o the passage (ldquoickyrdquo) or because it illogically attributes
agency to ood (ldquosinisterrdquo ldquosurlyrdquo)
QUESTION 17
Choice C is the best answer It accurately interprets ldquonot content to ollow
conventional business practicesrdquo as logically introducing the new practice o
ldquoemploying womenrdquo described in the ollowing sentences
Choices A B and D are incorrect because none recognizes why the sentence
is relevant to this particular location in the passage
QUESTION 18
Choice B is the best answer It is concise and ree o redundancies
Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and
ldquotremendousrdquo adjectives so close in meaning that together they present a
redundancy
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840
17
QUESTION 19
Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary
reerence to ldquosuch regulationsrdquo in the previous clause
Choices A B and C are incorrect because each lacks a necessary subject
such as a pronoun or noun
QUESTION 20
Choice C is the best answer It reers directly to benefits or the restaurantsrsquo
emale employees the subject o the previous sentence
Choices A B and D are incorrect because none logically builds upon the
sentence that precedes it
QUESTION 21
Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo
Choices A B and C are incorrect because each uses the punctuation or
a dependent clause (ldquoLiving independently and demonstrating an intense
work ethicrdquo) as i it were an independent clause
QUESTION 22
Choice A is the best answer It recognizes that the new inormation sup-
ports the previous sentencersquos claim that ldquothe Harvey Girls became known as
a transormative orcerdquo
Choices B C and D are incorrect because each misinterprets the relation-
ship between the proposed text and the passage
QUESTION 23
Choice A is the best answer It opens with a clause that identifies how
1-MCP affects apples which ocuses the sentence on 1-MCP as the subject
and allows the ideas in the sentence to progress logically
Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy
QUESTION 24
Choice D is the best answer Only the comma is necessary to separate
ldquoethylenerdquo rom the appositive noun phrase that defines it
Choices A B and C are incorrect because each creates a comma splice and
or adds unnecessary words
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1940
18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040
19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140
20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240
21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340
22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440
23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640
25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940
28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640
35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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10
QUESTION 38
Choice C is the best answer Wollstonecraf cites the statement made by
the authors o Passage 1 that excluding women rom political participation
is ldquoaccording to abstract principles impossible to explainrdquo (lines 61-65)
Wollstonecraf then states that i the authors o Passage 1 can discuss ldquothe
abstract rights o manrdquo they should be able to discuss the abstract rights owomen (lines 66-69) In these lines Wollstonecraf is developing her argument
by highlighting a flaw in the reasoning presented by the authors o Passage 1
Choices A B and D are incorrect because Wollstonecraf does not reer to
the statement made in Passage 1 to call into question the authorsrsquo qualifica-
tions dispute the assertion that women are excluded by their own govern-
ment (sentence one o Passage 1) or validate the authorsrsquo conclusions on
gender roles
QUESTION 39
Choice A is the best answer Te authors o Passage 1 argue that while
restricting womenrsquos reedoms may be ldquoimpossible to explainrdquo (line 7)
this restriction is necessary or societyrsquos overall happiness (lines 13-17)
Wollstonecraf however strongly challenges this argument asking the
authors o Passage 1 ldquoWho made man the exclusive judgerdquo o which ree-
doms are granted to women and likening societyrsquos male leaders to tyrants as
they deny women their ldquocivil and political rightsrdquo and leave them ldquogroping in
the darkrdquo (lines 78-88)
Choices B C and D are incorrect because they do not characterize the over-all relationship between Passage 1 and Passage 2
QUESTION 40
Choice D is the best answer Te authors o Passage 1 admit that women are
ldquoexcluded by the other hal [men] rom any participation in governmentrdquo
(lines 1-2) and Wollstonecraf states that societyrsquos male leaders create laws
that deny women ldquocivil and political rightsrdquo (line 86)
Choices A B and C are incorrect because the authors o both passages
would not agree that women had the same preerences as men required agood education or were as happy as men
QUESTION 41
Choice A is the best answer Wollstonecraf argues in the final paragraph
o Passage 2 that societyrsquos male leaders are like ldquotyrantsrdquo that deny women
ldquocivil and political rightsrdquo (lines 81-88) Te authors o Passage 1 would
most likely argue that allowing women these rights would be ldquoa reversal o
[societyrsquos] primary destinesrdquo as societyrsquos leaders should only seek womenrsquos
interests as they pertain to the ldquowishes o naturerdquo such as womenrsquos role as
7262019 PrepScholar Sat Practice Test 3 Answers
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11
mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created
two sexes or a particular reason so while men can exercise civil and politi-
cal rights women are not naturally suited to these activities (lines 30-36)
Choices B and C are incorrect because they are not supported by inorma-
tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do
not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo
QUESTION 42
Choice C is the best answer When discussing problems with bee colo-
nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo
(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-
tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a
tentative tone and provides urther evidence that the authors believe but are
not certain that their hypothesis is correct
Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone
QUESTION 43
Choice C is the best answer In lines 24-28 the authors hypothesize that bee
colonies will be susceptible to mite inestations i they do not occasionally
eed on pyrethrum producing plants In lines 42-46 they suggest creating a
trial where a ldquosmall number o commercial honey bee colonies are offered a
number o pyrethrum producing plantsrdquo to test their hypothesis
Choices A B and D are incorrect because the authors do not hypothesize that
honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees
to develop secondary inections that beekeepers should increase their use o
insecticides or that humans are more susceptible to varroa mites
QUESTION 44
Choice D is the best answer In lines 24-28 the authors provide evidence
that a bee colony may be more resistant to mite inections i the bees eat
pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-
nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees
Choices A B and C do not describe any o the authorsrsquo hypotheses
QUESTION 45
Choice D is the best answer Te authors explain that when beekeepers
use commercially produced insecticides to fight mite inections they may
ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-
cientrdquo (lines 31-35)
7262019 PrepScholar Sat Practice Test 3 Answers
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12
Choices A B and C are incorrect because the authors do not suggest that
beekeepersrsquo use o commercially produced insecticides increases mite popu-
lations kills bacteria or destroys beesrsquo primary ood source
QUESTION 46
Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-
ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo
Choices A B and D are incorrect because they do not provide the best evi-
dence that beekeepersrsquo use o commercially produced insecticides may be
harmul to bees choices A B and D ocus on mite inestationsrsquo impact on
honeybees
QUESTION 47
Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some
bees Te authors then state ldquoWe urther postulate that the proper dosage
necessary to prevent mite inestation may be better lef to the beesrdquo (lines
35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the
bees may naturally control mite inestations better than insecticides
Choices A C and D are incorrect because in this context ldquopostulaterdquo does
not mean to make an unounded assumption question a belie or theory or
conclude based on firm evidence
QUESTION 48
Choice B is the best answer In the ourth paragraph the authors propose
a trial to study i honeybeesrsquo consumption o pyrethrum producing plants
helps the honeybees deend against mite inestations In the experiment the
authors plan to offer honey bee colonies both pyrethrum producing plants
and ldquoa typical bee ood source such as cloverrdquo to determine i these different
diets affect the beesrsquo susceptibility to mite inestations
Choices A C and D are incorrect because the main purpose o the ourth
paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished
experiment
QUESTION 49
Choice A is the best answer In lines 43-45 the authors propose a scien-
tific trial in which honeybees are ldquooffered a number o pyrethrum producing
plants as well as a typical bee ood source such as cloverrdquo Since the authors
contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood
sourcerdquo it can be assumed that clover does not produce pyrethrums
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13
Choice B is incorrect because it is stated in the passage Choices C and D are
incorrect because they are not assumptions made by the authors
QUESTION 50
Choice B is the best answer Te table shows that 77 percent o the honeybee
colonies with colony collapse disorder were inected by all our pathogens
Choices A C and D are incorrect because they do not identiy the percent
o honeybee colonies with colony collapse disorder that were inected by all
our pathogens as based on data in the table
QUESTION 51
Choice D is the best answer Te table shows that 81 percent o colo-
nies without colony collapse disorder were affected by the pathogen
Nosema ceranae
Choices A B and C are incorrect because they do not identiy the pathogen
that inected the highest percentage o honeybee colonies without colony
collapse disorder as based on data in the table
QUESTION 52
Choice D is the best answer Te table discusses pathogen occurrence in
honeybee colonies but it includes no inormation as to whether these hon-
eybees were inected with mites Because the table does not suggest mites
inested the honeybee colonies no conclusions can be made as to whether
mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)
Choices A B and C are incorrect because the table provides no inormation
about whether these honeybees were inected with mites
Section 2 Writing and Language Test
QUESTION 1
Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-
ates a parallel structure within the list that begins with ldquohappierrdquo
Choices B C and D are incorrect because none creates a parallel structure
within the list o qualities
QUESTION 2
Choice B is the best answer Te ways in which exposure to natural light
affects employees is the main subject o the passage
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14
Choices A C and D are incorrect because none introduces the topic dis-
cussed in the remainder o the passage
QUESTION 3
Choice C is the best answer It accurately notes that the proposed sentence
would be placed directly between the first mention o circadian rhythms andthe explanation o the term
Choices A B and D are incorrect because each misinterprets the relation-
ship between the proposed additional text and the ideas in the paragraph
QUESTION 4
Choice C is the best answer It provides the correct possessive construction
or ldquobodyrdquo which must be a singular noun when discussed in general terms
as in this sentence Choice C also provides the correct plural construction
or ldquoclocksrdquo
Choices A B and D are incorrect because each applies either a possessive or
a plural construction in a place where it doesnrsquot belong
QUESTION 5
Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular
noun ldquoabsenteeismrdquo
Choices B C and D are incorrect because each provides a verb that
either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy
QUESTION 6
Choice B is the best answer It contains a direct reerence to productivity
the topic introduced in the previous sentence
Choices A C and D are incorrect because none directly addresses employee
productivity the primary subject o the previous sentence
QUESTION 7
Choice A is the best answer It opens with a reerence to lowered worker
productivity creating a transition rom the previous paragraph and clearly
positions the high energy costs o artificial light sources as an additional
disadvantage
Choices B C and D are incorrect because none o the choices offer an ade-
quate transition rom the previous paragraph Each awkwardly inserts the
issue o lower worker productivity into a statement about the high energy
costs o artificial light sources
7262019 PrepScholar Sat Practice Test 3 Answers
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15
QUESTION 8
Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-
cate that the savings occurred every year
Choices A B and C are incorrect because each proposes an option that
would result in a redundancy with ldquoannualrdquo
QUESTION 9
Choice C is the best answer It provides a transitional adverb that accurately
communicates that this sentence describes an option that companies could
choose (ldquolight tubesrdquo) instead o the option described in the previous sen-
tence (ldquoull-pane windowsrdquo)
Choices A B and D are incorrect because each proposes a transitional
adverb that does not accurately reflect the relationship between this sen-
tence and the one preceding it
QUESTION 10
Choice C is the best answer It provides the correct relative pronoun to cor-
respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-
duce the definition that ollows
Choices A B and D are incorrect because each offers a pronoun inappropri-
ate or opening a dependent clause defining ldquolight tubesrdquo
QUESTION 11
Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the
noun ldquomeansrdquo particularly as a way to connect it to another noun or verb
Choices A C and D are incorrect because each results in nonstandard
phrasing with ldquomeansrdquo
QUESTION 12
Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-
responds with the plural noun ldquosettlersrdquo
Choices B C and D are incorrect because each provides either a nonstan-
dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo
QUESTION 13
Choice C is the best answer It creates a transition rom the poor ood qual-
ity mentioned in the previous sentence to the inormation about Harvey in
the remainder o the sentence
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16
Choices A B and D are incorrect because none offers a transition rom the
previous sentence or a detail that corresponds precisely with the inorma-
tion in the remainder o the sentence
QUESTION 14
Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens
with a comma
Choices A B and C are incorrect because each proposes punctuation that
creates an inappropriately strong separation between the subject ldquoFred
Harveyrdquo and the verb ldquodecidedrdquo
QUESTION 15
Choice B is the best answer It provides the plural verb and plural posses-
sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo
Choices A C and D are incorrect because each either ails to provide a verb
that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide
the appropriate possessive pronoun
QUESTION 16
Choice C is the best answer It accurately echoes an earlier characterization
o the ood as being o ldquoterrible qualityrdquo while maintaining the established
tone o the passage
Choices A B and D are incorrect either because the word is less ormal than
the established tone o the passage (ldquoickyrdquo) or because it illogically attributes
agency to ood (ldquosinisterrdquo ldquosurlyrdquo)
QUESTION 17
Choice C is the best answer It accurately interprets ldquonot content to ollow
conventional business practicesrdquo as logically introducing the new practice o
ldquoemploying womenrdquo described in the ollowing sentences
Choices A B and D are incorrect because none recognizes why the sentence
is relevant to this particular location in the passage
QUESTION 18
Choice B is the best answer It is concise and ree o redundancies
Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and
ldquotremendousrdquo adjectives so close in meaning that together they present a
redundancy
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17
QUESTION 19
Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary
reerence to ldquosuch regulationsrdquo in the previous clause
Choices A B and C are incorrect because each lacks a necessary subject
such as a pronoun or noun
QUESTION 20
Choice C is the best answer It reers directly to benefits or the restaurantsrsquo
emale employees the subject o the previous sentence
Choices A B and D are incorrect because none logically builds upon the
sentence that precedes it
QUESTION 21
Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo
Choices A B and C are incorrect because each uses the punctuation or
a dependent clause (ldquoLiving independently and demonstrating an intense
work ethicrdquo) as i it were an independent clause
QUESTION 22
Choice A is the best answer It recognizes that the new inormation sup-
ports the previous sentencersquos claim that ldquothe Harvey Girls became known as
a transormative orcerdquo
Choices B C and D are incorrect because each misinterprets the relation-
ship between the proposed text and the passage
QUESTION 23
Choice A is the best answer It opens with a clause that identifies how
1-MCP affects apples which ocuses the sentence on 1-MCP as the subject
and allows the ideas in the sentence to progress logically
Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy
QUESTION 24
Choice D is the best answer Only the comma is necessary to separate
ldquoethylenerdquo rom the appositive noun phrase that defines it
Choices A B and C are incorrect because each creates a comma splice and
or adds unnecessary words
7262019 PrepScholar Sat Practice Test 3 Answers
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18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
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19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
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22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
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24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
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25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
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28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740
36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3840
37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040
QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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11
mothers (lines 18-30) Te authors o Passage 1 clariy that ldquonaturerdquo created
two sexes or a particular reason so while men can exercise civil and politi-
cal rights women are not naturally suited to these activities (lines 30-36)
Choices B and C are incorrect because they are not supported by inorma-
tion in Passage 1 Choice D is incorrect because the authors o Passage 1 do
not mention ldquonatural lawrdquo only the ldquowishes o naturerdquo
QUESTION 42
Choice C is the best answer When discussing problems with bee colo-
nies the authors use phrases like ldquowe suspectrdquo (line 19) and ldquowe postulaterdquo
(line 21) to show they are hypothesizing reasons or bee coloniesrsquo suscep-
tibility to mite inestations Te use o ldquocanrdquo ldquomayrdquo and ldquocouldrdquo creates a
tentative tone and provides urther evidence that the authors believe but are
not certain that their hypothesis is correct
Choices A B and D are incorrect because the authorsrsquo use o ldquocanrdquo ldquomayrdquoand ldquocouldrdquo does not create an optimistic dubious or critical tone
QUESTION 43
Choice C is the best answer In lines 24-28 the authors hypothesize that bee
colonies will be susceptible to mite inestations i they do not occasionally
eed on pyrethrum producing plants In lines 42-46 they suggest creating a
trial where a ldquosmall number o commercial honey bee colonies are offered a
number o pyrethrum producing plantsrdquo to test their hypothesis
Choices A B and D are incorrect because the authors do not hypothesize that
honeybeesrsquo exposure to both pyrethrums and mites will cause the honeybees
to develop secondary inections that beekeepers should increase their use o
insecticides or that humans are more susceptible to varroa mites
QUESTION 44
Choice D is the best answer In lines 24-28 the authors provide evidence
that a bee colony may be more resistant to mite inections i the bees eat
pyrethrums because this diet may help prevent bees rom becoming ldquoimmu-
nocompromised or nutritionally deficientrdquo In lines 42-50 the authors sug-gest testing this hypothesis in a trial on honeybees
Choices A B and C do not describe any o the authorsrsquo hypotheses
QUESTION 45
Choice D is the best answer Te authors explain that when beekeepers
use commercially produced insecticides to fight mite inections they may
ldquourther weakenrdquo bees that are ldquoimmunocompromised or nutritionally defi-
cientrdquo (lines 31-35)
7262019 PrepScholar Sat Practice Test 3 Answers
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12
Choices A B and C are incorrect because the authors do not suggest that
beekeepersrsquo use o commercially produced insecticides increases mite popu-
lations kills bacteria or destroys beesrsquo primary ood source
QUESTION 46
Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-
ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo
Choices A B and D are incorrect because they do not provide the best evi-
dence that beekeepersrsquo use o commercially produced insecticides may be
harmul to bees choices A B and D ocus on mite inestationsrsquo impact on
honeybees
QUESTION 47
Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some
bees Te authors then state ldquoWe urther postulate that the proper dosage
necessary to prevent mite inestation may be better lef to the beesrdquo (lines
35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the
bees may naturally control mite inestations better than insecticides
Choices A C and D are incorrect because in this context ldquopostulaterdquo does
not mean to make an unounded assumption question a belie or theory or
conclude based on firm evidence
QUESTION 48
Choice B is the best answer In the ourth paragraph the authors propose
a trial to study i honeybeesrsquo consumption o pyrethrum producing plants
helps the honeybees deend against mite inestations In the experiment the
authors plan to offer honey bee colonies both pyrethrum producing plants
and ldquoa typical bee ood source such as cloverrdquo to determine i these different
diets affect the beesrsquo susceptibility to mite inestations
Choices A C and D are incorrect because the main purpose o the ourth
paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished
experiment
QUESTION 49
Choice A is the best answer In lines 43-45 the authors propose a scien-
tific trial in which honeybees are ldquooffered a number o pyrethrum producing
plants as well as a typical bee ood source such as cloverrdquo Since the authors
contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood
sourcerdquo it can be assumed that clover does not produce pyrethrums
7262019 PrepScholar Sat Practice Test 3 Answers
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13
Choice B is incorrect because it is stated in the passage Choices C and D are
incorrect because they are not assumptions made by the authors
QUESTION 50
Choice B is the best answer Te table shows that 77 percent o the honeybee
colonies with colony collapse disorder were inected by all our pathogens
Choices A C and D are incorrect because they do not identiy the percent
o honeybee colonies with colony collapse disorder that were inected by all
our pathogens as based on data in the table
QUESTION 51
Choice D is the best answer Te table shows that 81 percent o colo-
nies without colony collapse disorder were affected by the pathogen
Nosema ceranae
Choices A B and C are incorrect because they do not identiy the pathogen
that inected the highest percentage o honeybee colonies without colony
collapse disorder as based on data in the table
QUESTION 52
Choice D is the best answer Te table discusses pathogen occurrence in
honeybee colonies but it includes no inormation as to whether these hon-
eybees were inected with mites Because the table does not suggest mites
inested the honeybee colonies no conclusions can be made as to whether
mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)
Choices A B and C are incorrect because the table provides no inormation
about whether these honeybees were inected with mites
Section 2 Writing and Language Test
QUESTION 1
Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-
ates a parallel structure within the list that begins with ldquohappierrdquo
Choices B C and D are incorrect because none creates a parallel structure
within the list o qualities
QUESTION 2
Choice B is the best answer Te ways in which exposure to natural light
affects employees is the main subject o the passage
7262019 PrepScholar Sat Practice Test 3 Answers
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14
Choices A C and D are incorrect because none introduces the topic dis-
cussed in the remainder o the passage
QUESTION 3
Choice C is the best answer It accurately notes that the proposed sentence
would be placed directly between the first mention o circadian rhythms andthe explanation o the term
Choices A B and D are incorrect because each misinterprets the relation-
ship between the proposed additional text and the ideas in the paragraph
QUESTION 4
Choice C is the best answer It provides the correct possessive construction
or ldquobodyrdquo which must be a singular noun when discussed in general terms
as in this sentence Choice C also provides the correct plural construction
or ldquoclocksrdquo
Choices A B and D are incorrect because each applies either a possessive or
a plural construction in a place where it doesnrsquot belong
QUESTION 5
Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular
noun ldquoabsenteeismrdquo
Choices B C and D are incorrect because each provides a verb that
either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy
QUESTION 6
Choice B is the best answer It contains a direct reerence to productivity
the topic introduced in the previous sentence
Choices A C and D are incorrect because none directly addresses employee
productivity the primary subject o the previous sentence
QUESTION 7
Choice A is the best answer It opens with a reerence to lowered worker
productivity creating a transition rom the previous paragraph and clearly
positions the high energy costs o artificial light sources as an additional
disadvantage
Choices B C and D are incorrect because none o the choices offer an ade-
quate transition rom the previous paragraph Each awkwardly inserts the
issue o lower worker productivity into a statement about the high energy
costs o artificial light sources
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1640
15
QUESTION 8
Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-
cate that the savings occurred every year
Choices A B and C are incorrect because each proposes an option that
would result in a redundancy with ldquoannualrdquo
QUESTION 9
Choice C is the best answer It provides a transitional adverb that accurately
communicates that this sentence describes an option that companies could
choose (ldquolight tubesrdquo) instead o the option described in the previous sen-
tence (ldquoull-pane windowsrdquo)
Choices A B and D are incorrect because each proposes a transitional
adverb that does not accurately reflect the relationship between this sen-
tence and the one preceding it
QUESTION 10
Choice C is the best answer It provides the correct relative pronoun to cor-
respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-
duce the definition that ollows
Choices A B and D are incorrect because each offers a pronoun inappropri-
ate or opening a dependent clause defining ldquolight tubesrdquo
QUESTION 11
Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the
noun ldquomeansrdquo particularly as a way to connect it to another noun or verb
Choices A C and D are incorrect because each results in nonstandard
phrasing with ldquomeansrdquo
QUESTION 12
Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-
responds with the plural noun ldquosettlersrdquo
Choices B C and D are incorrect because each provides either a nonstan-
dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo
QUESTION 13
Choice C is the best answer It creates a transition rom the poor ood qual-
ity mentioned in the previous sentence to the inormation about Harvey in
the remainder o the sentence
7262019 PrepScholar Sat Practice Test 3 Answers
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16
Choices A B and D are incorrect because none offers a transition rom the
previous sentence or a detail that corresponds precisely with the inorma-
tion in the remainder o the sentence
QUESTION 14
Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens
with a comma
Choices A B and C are incorrect because each proposes punctuation that
creates an inappropriately strong separation between the subject ldquoFred
Harveyrdquo and the verb ldquodecidedrdquo
QUESTION 15
Choice B is the best answer It provides the plural verb and plural posses-
sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo
Choices A C and D are incorrect because each either ails to provide a verb
that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide
the appropriate possessive pronoun
QUESTION 16
Choice C is the best answer It accurately echoes an earlier characterization
o the ood as being o ldquoterrible qualityrdquo while maintaining the established
tone o the passage
Choices A B and D are incorrect either because the word is less ormal than
the established tone o the passage (ldquoickyrdquo) or because it illogically attributes
agency to ood (ldquosinisterrdquo ldquosurlyrdquo)
QUESTION 17
Choice C is the best answer It accurately interprets ldquonot content to ollow
conventional business practicesrdquo as logically introducing the new practice o
ldquoemploying womenrdquo described in the ollowing sentences
Choices A B and D are incorrect because none recognizes why the sentence
is relevant to this particular location in the passage
QUESTION 18
Choice B is the best answer It is concise and ree o redundancies
Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and
ldquotremendousrdquo adjectives so close in meaning that together they present a
redundancy
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840
17
QUESTION 19
Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary
reerence to ldquosuch regulationsrdquo in the previous clause
Choices A B and C are incorrect because each lacks a necessary subject
such as a pronoun or noun
QUESTION 20
Choice C is the best answer It reers directly to benefits or the restaurantsrsquo
emale employees the subject o the previous sentence
Choices A B and D are incorrect because none logically builds upon the
sentence that precedes it
QUESTION 21
Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo
Choices A B and C are incorrect because each uses the punctuation or
a dependent clause (ldquoLiving independently and demonstrating an intense
work ethicrdquo) as i it were an independent clause
QUESTION 22
Choice A is the best answer It recognizes that the new inormation sup-
ports the previous sentencersquos claim that ldquothe Harvey Girls became known as
a transormative orcerdquo
Choices B C and D are incorrect because each misinterprets the relation-
ship between the proposed text and the passage
QUESTION 23
Choice A is the best answer It opens with a clause that identifies how
1-MCP affects apples which ocuses the sentence on 1-MCP as the subject
and allows the ideas in the sentence to progress logically
Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy
QUESTION 24
Choice D is the best answer Only the comma is necessary to separate
ldquoethylenerdquo rom the appositive noun phrase that defines it
Choices A B and C are incorrect because each creates a comma splice and
or adds unnecessary words
7262019 PrepScholar Sat Practice Test 3 Answers
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18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
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19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240
21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340
22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440
23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640
25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
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26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940
28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040
29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3140
30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3240
31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3340
32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3440
33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3540
34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640
35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740
36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3840
37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3940
38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040
QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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12
Choices A B and C are incorrect because the authors do not suggest that
beekeepersrsquo use o commercially produced insecticides increases mite popu-
lations kills bacteria or destroys beesrsquo primary ood source
QUESTION 46
Choice C is the best answer In lines 31-35 the authors provide evidencethat beekeepersrsquo use o commercially produced insecticides may cause ur-
ther harm to ldquoimmunocompromised or nutritionally deficient beesrdquo
Choices A B and D are incorrect because they do not provide the best evi-
dence that beekeepersrsquo use o commercially produced insecticides may be
harmul to bees choices A B and D ocus on mite inestationsrsquo impact on
honeybees
QUESTION 47
Choice B is the best answer In lines 31-35 the authors argue that beekeep-ersrsquo use o insecticides to control mite inestations may be harmul to some
bees Te authors then state ldquoWe urther postulate that the proper dosage
necessary to prevent mite inestation may be better lef to the beesrdquo (lines
35-37) In this context the authors ldquopostulaterdquo or put orth the idea that the
bees may naturally control mite inestations better than insecticides
Choices A C and D are incorrect because in this context ldquopostulaterdquo does
not mean to make an unounded assumption question a belie or theory or
conclude based on firm evidence
QUESTION 48
Choice B is the best answer In the ourth paragraph the authors propose
a trial to study i honeybeesrsquo consumption o pyrethrum producing plants
helps the honeybees deend against mite inestations In the experiment the
authors plan to offer honey bee colonies both pyrethrum producing plants
and ldquoa typical bee ood source such as cloverrdquo to determine i these different
diets affect the beesrsquo susceptibility to mite inestations
Choices A C and D are incorrect because the main purpose o the ourth
paragraph is not to summarize the results o an experiment provide acomparative nutritional analysis or predict an outcome o an unfinished
experiment
QUESTION 49
Choice A is the best answer In lines 43-45 the authors propose a scien-
tific trial in which honeybees are ldquooffered a number o pyrethrum producing
plants as well as a typical bee ood source such as cloverrdquo Since the authors
contrast the ldquopyrethrum producing plantsrdquo with clover a ldquotypical bee ood
sourcerdquo it can be assumed that clover does not produce pyrethrums
7262019 PrepScholar Sat Practice Test 3 Answers
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13
Choice B is incorrect because it is stated in the passage Choices C and D are
incorrect because they are not assumptions made by the authors
QUESTION 50
Choice B is the best answer Te table shows that 77 percent o the honeybee
colonies with colony collapse disorder were inected by all our pathogens
Choices A C and D are incorrect because they do not identiy the percent
o honeybee colonies with colony collapse disorder that were inected by all
our pathogens as based on data in the table
QUESTION 51
Choice D is the best answer Te table shows that 81 percent o colo-
nies without colony collapse disorder were affected by the pathogen
Nosema ceranae
Choices A B and C are incorrect because they do not identiy the pathogen
that inected the highest percentage o honeybee colonies without colony
collapse disorder as based on data in the table
QUESTION 52
Choice D is the best answer Te table discusses pathogen occurrence in
honeybee colonies but it includes no inormation as to whether these hon-
eybees were inected with mites Because the table does not suggest mites
inested the honeybee colonies no conclusions can be made as to whether
mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)
Choices A B and C are incorrect because the table provides no inormation
about whether these honeybees were inected with mites
Section 2 Writing and Language Test
QUESTION 1
Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-
ates a parallel structure within the list that begins with ldquohappierrdquo
Choices B C and D are incorrect because none creates a parallel structure
within the list o qualities
QUESTION 2
Choice B is the best answer Te ways in which exposure to natural light
affects employees is the main subject o the passage
7262019 PrepScholar Sat Practice Test 3 Answers
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14
Choices A C and D are incorrect because none introduces the topic dis-
cussed in the remainder o the passage
QUESTION 3
Choice C is the best answer It accurately notes that the proposed sentence
would be placed directly between the first mention o circadian rhythms andthe explanation o the term
Choices A B and D are incorrect because each misinterprets the relation-
ship between the proposed additional text and the ideas in the paragraph
QUESTION 4
Choice C is the best answer It provides the correct possessive construction
or ldquobodyrdquo which must be a singular noun when discussed in general terms
as in this sentence Choice C also provides the correct plural construction
or ldquoclocksrdquo
Choices A B and D are incorrect because each applies either a possessive or
a plural construction in a place where it doesnrsquot belong
QUESTION 5
Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular
noun ldquoabsenteeismrdquo
Choices B C and D are incorrect because each provides a verb that
either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy
QUESTION 6
Choice B is the best answer It contains a direct reerence to productivity
the topic introduced in the previous sentence
Choices A C and D are incorrect because none directly addresses employee
productivity the primary subject o the previous sentence
QUESTION 7
Choice A is the best answer It opens with a reerence to lowered worker
productivity creating a transition rom the previous paragraph and clearly
positions the high energy costs o artificial light sources as an additional
disadvantage
Choices B C and D are incorrect because none o the choices offer an ade-
quate transition rom the previous paragraph Each awkwardly inserts the
issue o lower worker productivity into a statement about the high energy
costs o artificial light sources
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1640
15
QUESTION 8
Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-
cate that the savings occurred every year
Choices A B and C are incorrect because each proposes an option that
would result in a redundancy with ldquoannualrdquo
QUESTION 9
Choice C is the best answer It provides a transitional adverb that accurately
communicates that this sentence describes an option that companies could
choose (ldquolight tubesrdquo) instead o the option described in the previous sen-
tence (ldquoull-pane windowsrdquo)
Choices A B and D are incorrect because each proposes a transitional
adverb that does not accurately reflect the relationship between this sen-
tence and the one preceding it
QUESTION 10
Choice C is the best answer It provides the correct relative pronoun to cor-
respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-
duce the definition that ollows
Choices A B and D are incorrect because each offers a pronoun inappropri-
ate or opening a dependent clause defining ldquolight tubesrdquo
QUESTION 11
Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the
noun ldquomeansrdquo particularly as a way to connect it to another noun or verb
Choices A C and D are incorrect because each results in nonstandard
phrasing with ldquomeansrdquo
QUESTION 12
Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-
responds with the plural noun ldquosettlersrdquo
Choices B C and D are incorrect because each provides either a nonstan-
dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo
QUESTION 13
Choice C is the best answer It creates a transition rom the poor ood qual-
ity mentioned in the previous sentence to the inormation about Harvey in
the remainder o the sentence
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1740
16
Choices A B and D are incorrect because none offers a transition rom the
previous sentence or a detail that corresponds precisely with the inorma-
tion in the remainder o the sentence
QUESTION 14
Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens
with a comma
Choices A B and C are incorrect because each proposes punctuation that
creates an inappropriately strong separation between the subject ldquoFred
Harveyrdquo and the verb ldquodecidedrdquo
QUESTION 15
Choice B is the best answer It provides the plural verb and plural posses-
sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo
Choices A C and D are incorrect because each either ails to provide a verb
that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide
the appropriate possessive pronoun
QUESTION 16
Choice C is the best answer It accurately echoes an earlier characterization
o the ood as being o ldquoterrible qualityrdquo while maintaining the established
tone o the passage
Choices A B and D are incorrect either because the word is less ormal than
the established tone o the passage (ldquoickyrdquo) or because it illogically attributes
agency to ood (ldquosinisterrdquo ldquosurlyrdquo)
QUESTION 17
Choice C is the best answer It accurately interprets ldquonot content to ollow
conventional business practicesrdquo as logically introducing the new practice o
ldquoemploying womenrdquo described in the ollowing sentences
Choices A B and D are incorrect because none recognizes why the sentence
is relevant to this particular location in the passage
QUESTION 18
Choice B is the best answer It is concise and ree o redundancies
Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and
ldquotremendousrdquo adjectives so close in meaning that together they present a
redundancy
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840
17
QUESTION 19
Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary
reerence to ldquosuch regulationsrdquo in the previous clause
Choices A B and C are incorrect because each lacks a necessary subject
such as a pronoun or noun
QUESTION 20
Choice C is the best answer It reers directly to benefits or the restaurantsrsquo
emale employees the subject o the previous sentence
Choices A B and D are incorrect because none logically builds upon the
sentence that precedes it
QUESTION 21
Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo
Choices A B and C are incorrect because each uses the punctuation or
a dependent clause (ldquoLiving independently and demonstrating an intense
work ethicrdquo) as i it were an independent clause
QUESTION 22
Choice A is the best answer It recognizes that the new inormation sup-
ports the previous sentencersquos claim that ldquothe Harvey Girls became known as
a transormative orcerdquo
Choices B C and D are incorrect because each misinterprets the relation-
ship between the proposed text and the passage
QUESTION 23
Choice A is the best answer It opens with a clause that identifies how
1-MCP affects apples which ocuses the sentence on 1-MCP as the subject
and allows the ideas in the sentence to progress logically
Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy
QUESTION 24
Choice D is the best answer Only the comma is necessary to separate
ldquoethylenerdquo rom the appositive noun phrase that defines it
Choices A B and C are incorrect because each creates a comma splice and
or adds unnecessary words
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1940
18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040
19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140
20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240
21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340
22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440
23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640
25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940
28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040
29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3340
32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640
35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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13
Choice B is incorrect because it is stated in the passage Choices C and D are
incorrect because they are not assumptions made by the authors
QUESTION 50
Choice B is the best answer Te table shows that 77 percent o the honeybee
colonies with colony collapse disorder were inected by all our pathogens
Choices A C and D are incorrect because they do not identiy the percent
o honeybee colonies with colony collapse disorder that were inected by all
our pathogens as based on data in the table
QUESTION 51
Choice D is the best answer Te table shows that 81 percent o colo-
nies without colony collapse disorder were affected by the pathogen
Nosema ceranae
Choices A B and C are incorrect because they do not identiy the pathogen
that inected the highest percentage o honeybee colonies without colony
collapse disorder as based on data in the table
QUESTION 52
Choice D is the best answer Te table discusses pathogen occurrence in
honeybee colonies but it includes no inormation as to whether these hon-
eybees were inected with mites Because the table does not suggest mites
inested the honeybee colonies no conclusions can be made as to whether
mites increased the honeybeesrsquo ldquosusceptibility to secondary inection withungi bacteria or virusesrdquo (lines 4-5)
Choices A B and C are incorrect because the table provides no inormation
about whether these honeybees were inected with mites
Section 2 Writing and Language Test
QUESTION 1
Choice A is the best answer because by providing the comparative adjectiveldquohealthierrdquo and the word ldquomorerdquo to make ldquoproductiverdquo comparative it cre-
ates a parallel structure within the list that begins with ldquohappierrdquo
Choices B C and D are incorrect because none creates a parallel structure
within the list o qualities
QUESTION 2
Choice B is the best answer Te ways in which exposure to natural light
affects employees is the main subject o the passage
7262019 PrepScholar Sat Practice Test 3 Answers
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14
Choices A C and D are incorrect because none introduces the topic dis-
cussed in the remainder o the passage
QUESTION 3
Choice C is the best answer It accurately notes that the proposed sentence
would be placed directly between the first mention o circadian rhythms andthe explanation o the term
Choices A B and D are incorrect because each misinterprets the relation-
ship between the proposed additional text and the ideas in the paragraph
QUESTION 4
Choice C is the best answer It provides the correct possessive construction
or ldquobodyrdquo which must be a singular noun when discussed in general terms
as in this sentence Choice C also provides the correct plural construction
or ldquoclocksrdquo
Choices A B and D are incorrect because each applies either a possessive or
a plural construction in a place where it doesnrsquot belong
QUESTION 5
Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular
noun ldquoabsenteeismrdquo
Choices B C and D are incorrect because each provides a verb that
either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy
QUESTION 6
Choice B is the best answer It contains a direct reerence to productivity
the topic introduced in the previous sentence
Choices A C and D are incorrect because none directly addresses employee
productivity the primary subject o the previous sentence
QUESTION 7
Choice A is the best answer It opens with a reerence to lowered worker
productivity creating a transition rom the previous paragraph and clearly
positions the high energy costs o artificial light sources as an additional
disadvantage
Choices B C and D are incorrect because none o the choices offer an ade-
quate transition rom the previous paragraph Each awkwardly inserts the
issue o lower worker productivity into a statement about the high energy
costs o artificial light sources
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1640
15
QUESTION 8
Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-
cate that the savings occurred every year
Choices A B and C are incorrect because each proposes an option that
would result in a redundancy with ldquoannualrdquo
QUESTION 9
Choice C is the best answer It provides a transitional adverb that accurately
communicates that this sentence describes an option that companies could
choose (ldquolight tubesrdquo) instead o the option described in the previous sen-
tence (ldquoull-pane windowsrdquo)
Choices A B and D are incorrect because each proposes a transitional
adverb that does not accurately reflect the relationship between this sen-
tence and the one preceding it
QUESTION 10
Choice C is the best answer It provides the correct relative pronoun to cor-
respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-
duce the definition that ollows
Choices A B and D are incorrect because each offers a pronoun inappropri-
ate or opening a dependent clause defining ldquolight tubesrdquo
QUESTION 11
Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the
noun ldquomeansrdquo particularly as a way to connect it to another noun or verb
Choices A C and D are incorrect because each results in nonstandard
phrasing with ldquomeansrdquo
QUESTION 12
Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-
responds with the plural noun ldquosettlersrdquo
Choices B C and D are incorrect because each provides either a nonstan-
dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo
QUESTION 13
Choice C is the best answer It creates a transition rom the poor ood qual-
ity mentioned in the previous sentence to the inormation about Harvey in
the remainder o the sentence
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1740
16
Choices A B and D are incorrect because none offers a transition rom the
previous sentence or a detail that corresponds precisely with the inorma-
tion in the remainder o the sentence
QUESTION 14
Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens
with a comma
Choices A B and C are incorrect because each proposes punctuation that
creates an inappropriately strong separation between the subject ldquoFred
Harveyrdquo and the verb ldquodecidedrdquo
QUESTION 15
Choice B is the best answer It provides the plural verb and plural posses-
sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo
Choices A C and D are incorrect because each either ails to provide a verb
that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide
the appropriate possessive pronoun
QUESTION 16
Choice C is the best answer It accurately echoes an earlier characterization
o the ood as being o ldquoterrible qualityrdquo while maintaining the established
tone o the passage
Choices A B and D are incorrect either because the word is less ormal than
the established tone o the passage (ldquoickyrdquo) or because it illogically attributes
agency to ood (ldquosinisterrdquo ldquosurlyrdquo)
QUESTION 17
Choice C is the best answer It accurately interprets ldquonot content to ollow
conventional business practicesrdquo as logically introducing the new practice o
ldquoemploying womenrdquo described in the ollowing sentences
Choices A B and D are incorrect because none recognizes why the sentence
is relevant to this particular location in the passage
QUESTION 18
Choice B is the best answer It is concise and ree o redundancies
Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and
ldquotremendousrdquo adjectives so close in meaning that together they present a
redundancy
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840
17
QUESTION 19
Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary
reerence to ldquosuch regulationsrdquo in the previous clause
Choices A B and C are incorrect because each lacks a necessary subject
such as a pronoun or noun
QUESTION 20
Choice C is the best answer It reers directly to benefits or the restaurantsrsquo
emale employees the subject o the previous sentence
Choices A B and D are incorrect because none logically builds upon the
sentence that precedes it
QUESTION 21
Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo
Choices A B and C are incorrect because each uses the punctuation or
a dependent clause (ldquoLiving independently and demonstrating an intense
work ethicrdquo) as i it were an independent clause
QUESTION 22
Choice A is the best answer It recognizes that the new inormation sup-
ports the previous sentencersquos claim that ldquothe Harvey Girls became known as
a transormative orcerdquo
Choices B C and D are incorrect because each misinterprets the relation-
ship between the proposed text and the passage
QUESTION 23
Choice A is the best answer It opens with a clause that identifies how
1-MCP affects apples which ocuses the sentence on 1-MCP as the subject
and allows the ideas in the sentence to progress logically
Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy
QUESTION 24
Choice D is the best answer Only the comma is necessary to separate
ldquoethylenerdquo rom the appositive noun phrase that defines it
Choices A B and C are incorrect because each creates a comma splice and
or adds unnecessary words
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1940
18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040
19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140
20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240
21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340
22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440
23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640
25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940
28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1540
14
Choices A C and D are incorrect because none introduces the topic dis-
cussed in the remainder o the passage
QUESTION 3
Choice C is the best answer It accurately notes that the proposed sentence
would be placed directly between the first mention o circadian rhythms andthe explanation o the term
Choices A B and D are incorrect because each misinterprets the relation-
ship between the proposed additional text and the ideas in the paragraph
QUESTION 4
Choice C is the best answer It provides the correct possessive construction
or ldquobodyrdquo which must be a singular noun when discussed in general terms
as in this sentence Choice C also provides the correct plural construction
or ldquoclocksrdquo
Choices A B and D are incorrect because each applies either a possessive or
a plural construction in a place where it doesnrsquot belong
QUESTION 5
Choice A is the best answer Te singular verb ldquoisrdquo agrees with the singular
noun ldquoabsenteeismrdquo
Choices B C and D are incorrect because each provides a verb that
either ails to agree with the singular subject ldquoabsenteeismrdquo or introducesredundancy
QUESTION 6
Choice B is the best answer It contains a direct reerence to productivity
the topic introduced in the previous sentence
Choices A C and D are incorrect because none directly addresses employee
productivity the primary subject o the previous sentence
QUESTION 7
Choice A is the best answer It opens with a reerence to lowered worker
productivity creating a transition rom the previous paragraph and clearly
positions the high energy costs o artificial light sources as an additional
disadvantage
Choices B C and D are incorrect because none o the choices offer an ade-
quate transition rom the previous paragraph Each awkwardly inserts the
issue o lower worker productivity into a statement about the high energy
costs o artificial light sources
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1640
15
QUESTION 8
Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-
cate that the savings occurred every year
Choices A B and C are incorrect because each proposes an option that
would result in a redundancy with ldquoannualrdquo
QUESTION 9
Choice C is the best answer It provides a transitional adverb that accurately
communicates that this sentence describes an option that companies could
choose (ldquolight tubesrdquo) instead o the option described in the previous sen-
tence (ldquoull-pane windowsrdquo)
Choices A B and D are incorrect because each proposes a transitional
adverb that does not accurately reflect the relationship between this sen-
tence and the one preceding it
QUESTION 10
Choice C is the best answer It provides the correct relative pronoun to cor-
respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-
duce the definition that ollows
Choices A B and D are incorrect because each offers a pronoun inappropri-
ate or opening a dependent clause defining ldquolight tubesrdquo
QUESTION 11
Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the
noun ldquomeansrdquo particularly as a way to connect it to another noun or verb
Choices A C and D are incorrect because each results in nonstandard
phrasing with ldquomeansrdquo
QUESTION 12
Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-
responds with the plural noun ldquosettlersrdquo
Choices B C and D are incorrect because each provides either a nonstan-
dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo
QUESTION 13
Choice C is the best answer It creates a transition rom the poor ood qual-
ity mentioned in the previous sentence to the inormation about Harvey in
the remainder o the sentence
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1740
16
Choices A B and D are incorrect because none offers a transition rom the
previous sentence or a detail that corresponds precisely with the inorma-
tion in the remainder o the sentence
QUESTION 14
Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens
with a comma
Choices A B and C are incorrect because each proposes punctuation that
creates an inappropriately strong separation between the subject ldquoFred
Harveyrdquo and the verb ldquodecidedrdquo
QUESTION 15
Choice B is the best answer It provides the plural verb and plural posses-
sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo
Choices A C and D are incorrect because each either ails to provide a verb
that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide
the appropriate possessive pronoun
QUESTION 16
Choice C is the best answer It accurately echoes an earlier characterization
o the ood as being o ldquoterrible qualityrdquo while maintaining the established
tone o the passage
Choices A B and D are incorrect either because the word is less ormal than
the established tone o the passage (ldquoickyrdquo) or because it illogically attributes
agency to ood (ldquosinisterrdquo ldquosurlyrdquo)
QUESTION 17
Choice C is the best answer It accurately interprets ldquonot content to ollow
conventional business practicesrdquo as logically introducing the new practice o
ldquoemploying womenrdquo described in the ollowing sentences
Choices A B and D are incorrect because none recognizes why the sentence
is relevant to this particular location in the passage
QUESTION 18
Choice B is the best answer It is concise and ree o redundancies
Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and
ldquotremendousrdquo adjectives so close in meaning that together they present a
redundancy
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840
17
QUESTION 19
Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary
reerence to ldquosuch regulationsrdquo in the previous clause
Choices A B and C are incorrect because each lacks a necessary subject
such as a pronoun or noun
QUESTION 20
Choice C is the best answer It reers directly to benefits or the restaurantsrsquo
emale employees the subject o the previous sentence
Choices A B and D are incorrect because none logically builds upon the
sentence that precedes it
QUESTION 21
Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo
Choices A B and C are incorrect because each uses the punctuation or
a dependent clause (ldquoLiving independently and demonstrating an intense
work ethicrdquo) as i it were an independent clause
QUESTION 22
Choice A is the best answer It recognizes that the new inormation sup-
ports the previous sentencersquos claim that ldquothe Harvey Girls became known as
a transormative orcerdquo
Choices B C and D are incorrect because each misinterprets the relation-
ship between the proposed text and the passage
QUESTION 23
Choice A is the best answer It opens with a clause that identifies how
1-MCP affects apples which ocuses the sentence on 1-MCP as the subject
and allows the ideas in the sentence to progress logically
Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy
QUESTION 24
Choice D is the best answer Only the comma is necessary to separate
ldquoethylenerdquo rom the appositive noun phrase that defines it
Choices A B and C are incorrect because each creates a comma splice and
or adds unnecessary words
7262019 PrepScholar Sat Practice Test 3 Answers
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18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040
19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340
22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440
23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640
25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940
28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040
29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040
QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1640
15
QUESTION 8
Choice D is the best answer Te word ldquoannualrdquo is adequate to communi-
cate that the savings occurred every year
Choices A B and C are incorrect because each proposes an option that
would result in a redundancy with ldquoannualrdquo
QUESTION 9
Choice C is the best answer It provides a transitional adverb that accurately
communicates that this sentence describes an option that companies could
choose (ldquolight tubesrdquo) instead o the option described in the previous sen-
tence (ldquoull-pane windowsrdquo)
Choices A B and D are incorrect because each proposes a transitional
adverb that does not accurately reflect the relationship between this sen-
tence and the one preceding it
QUESTION 10
Choice C is the best answer It provides the correct relative pronoun to cor-
respond with the plural reerent ldquolight tubesrdquo and the correct verb to intro-
duce the definition that ollows
Choices A B and D are incorrect because each offers a pronoun inappropri-
ate or opening a dependent clause defining ldquolight tubesrdquo
QUESTION 11
Choice B is the best answer Te preposition ldquoordquo idiomatically ollows the
noun ldquomeansrdquo particularly as a way to connect it to another noun or verb
Choices A C and D are incorrect because each results in nonstandard
phrasing with ldquomeansrdquo
QUESTION 12
Choice A is the best answer Te plural reflexive pronoun ldquothemselvesrdquo cor-
responds with the plural noun ldquosettlersrdquo
Choices B C and D are incorrect because each provides either a nonstan-
dard phrase or a singular pronoun that does not correspond with ldquosettlersrdquo
QUESTION 13
Choice C is the best answer It creates a transition rom the poor ood qual-
ity mentioned in the previous sentence to the inormation about Harvey in
the remainder o the sentence
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1740
16
Choices A B and D are incorrect because none offers a transition rom the
previous sentence or a detail that corresponds precisely with the inorma-
tion in the remainder o the sentence
QUESTION 14
Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens
with a comma
Choices A B and C are incorrect because each proposes punctuation that
creates an inappropriately strong separation between the subject ldquoFred
Harveyrdquo and the verb ldquodecidedrdquo
QUESTION 15
Choice B is the best answer It provides the plural verb and plural posses-
sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo
Choices A C and D are incorrect because each either ails to provide a verb
that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide
the appropriate possessive pronoun
QUESTION 16
Choice C is the best answer It accurately echoes an earlier characterization
o the ood as being o ldquoterrible qualityrdquo while maintaining the established
tone o the passage
Choices A B and D are incorrect either because the word is less ormal than
the established tone o the passage (ldquoickyrdquo) or because it illogically attributes
agency to ood (ldquosinisterrdquo ldquosurlyrdquo)
QUESTION 17
Choice C is the best answer It accurately interprets ldquonot content to ollow
conventional business practicesrdquo as logically introducing the new practice o
ldquoemploying womenrdquo described in the ollowing sentences
Choices A B and D are incorrect because none recognizes why the sentence
is relevant to this particular location in the passage
QUESTION 18
Choice B is the best answer It is concise and ree o redundancies
Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and
ldquotremendousrdquo adjectives so close in meaning that together they present a
redundancy
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840
17
QUESTION 19
Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary
reerence to ldquosuch regulationsrdquo in the previous clause
Choices A B and C are incorrect because each lacks a necessary subject
such as a pronoun or noun
QUESTION 20
Choice C is the best answer It reers directly to benefits or the restaurantsrsquo
emale employees the subject o the previous sentence
Choices A B and D are incorrect because none logically builds upon the
sentence that precedes it
QUESTION 21
Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo
Choices A B and C are incorrect because each uses the punctuation or
a dependent clause (ldquoLiving independently and demonstrating an intense
work ethicrdquo) as i it were an independent clause
QUESTION 22
Choice A is the best answer It recognizes that the new inormation sup-
ports the previous sentencersquos claim that ldquothe Harvey Girls became known as
a transormative orcerdquo
Choices B C and D are incorrect because each misinterprets the relation-
ship between the proposed text and the passage
QUESTION 23
Choice A is the best answer It opens with a clause that identifies how
1-MCP affects apples which ocuses the sentence on 1-MCP as the subject
and allows the ideas in the sentence to progress logically
Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy
QUESTION 24
Choice D is the best answer Only the comma is necessary to separate
ldquoethylenerdquo rom the appositive noun phrase that defines it
Choices A B and C are incorrect because each creates a comma splice and
or adds unnecessary words
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1940
18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040
19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140
20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240
21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340
22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440
23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640
25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940
28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040
29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040
QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1740
16
Choices A B and D are incorrect because none offers a transition rom the
previous sentence or a detail that corresponds precisely with the inorma-
tion in the remainder o the sentence
QUESTION 14
Choice D is the best answer It correctly provides a comma to closethe modiying clause ldquoan English-born entrepreneurrdquo which opens
with a comma
Choices A B and C are incorrect because each proposes punctuation that
creates an inappropriately strong separation between the subject ldquoFred
Harveyrdquo and the verb ldquodecidedrdquo
QUESTION 15
Choice B is the best answer It provides the plural verb and plural posses-
sive pronoun that grammatically correspond to the plural reerent ldquoHarveyHousesrdquo
Choices A C and D are incorrect because each either ails to provide a verb
that corresponds with the plural reerent ldquoHarvey Housesrdquo or ails to provide
the appropriate possessive pronoun
QUESTION 16
Choice C is the best answer It accurately echoes an earlier characterization
o the ood as being o ldquoterrible qualityrdquo while maintaining the established
tone o the passage
Choices A B and D are incorrect either because the word is less ormal than
the established tone o the passage (ldquoickyrdquo) or because it illogically attributes
agency to ood (ldquosinisterrdquo ldquosurlyrdquo)
QUESTION 17
Choice C is the best answer It accurately interprets ldquonot content to ollow
conventional business practicesrdquo as logically introducing the new practice o
ldquoemploying womenrdquo described in the ollowing sentences
Choices A B and D are incorrect because none recognizes why the sentence
is relevant to this particular location in the passage
QUESTION 18
Choice B is the best answer It is concise and ree o redundancies
Choices A C and D are incorrect because each pairs ldquooverwhelmingrdquo and
ldquotremendousrdquo adjectives so close in meaning that together they present a
redundancy
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840
17
QUESTION 19
Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary
reerence to ldquosuch regulationsrdquo in the previous clause
Choices A B and C are incorrect because each lacks a necessary subject
such as a pronoun or noun
QUESTION 20
Choice C is the best answer It reers directly to benefits or the restaurantsrsquo
emale employees the subject o the previous sentence
Choices A B and D are incorrect because none logically builds upon the
sentence that precedes it
QUESTION 21
Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo
Choices A B and C are incorrect because each uses the punctuation or
a dependent clause (ldquoLiving independently and demonstrating an intense
work ethicrdquo) as i it were an independent clause
QUESTION 22
Choice A is the best answer It recognizes that the new inormation sup-
ports the previous sentencersquos claim that ldquothe Harvey Girls became known as
a transormative orcerdquo
Choices B C and D are incorrect because each misinterprets the relation-
ship between the proposed text and the passage
QUESTION 23
Choice A is the best answer It opens with a clause that identifies how
1-MCP affects apples which ocuses the sentence on 1-MCP as the subject
and allows the ideas in the sentence to progress logically
Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy
QUESTION 24
Choice D is the best answer Only the comma is necessary to separate
ldquoethylenerdquo rom the appositive noun phrase that defines it
Choices A B and C are incorrect because each creates a comma splice and
or adds unnecessary words
7262019 PrepScholar Sat Practice Test 3 Answers
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18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040
19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140
20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240
21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340
22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440
23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640
25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
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28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
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29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040
QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1840
17
QUESTION 19
Choice D is the best answer It contains the pronoun ldquotheyrdquo a necessary
reerence to ldquosuch regulationsrdquo in the previous clause
Choices A B and C are incorrect because each lacks a necessary subject
such as a pronoun or noun
QUESTION 20
Choice C is the best answer It reers directly to benefits or the restaurantsrsquo
emale employees the subject o the previous sentence
Choices A B and D are incorrect because none logically builds upon the
sentence that precedes it
QUESTION 21
Choice D is the best answer It provides punctuation that indicates that theopening dependent clause modifies the subject ldquoHarvey Girlsrdquo
Choices A B and C are incorrect because each uses the punctuation or
a dependent clause (ldquoLiving independently and demonstrating an intense
work ethicrdquo) as i it were an independent clause
QUESTION 22
Choice A is the best answer It recognizes that the new inormation sup-
ports the previous sentencersquos claim that ldquothe Harvey Girls became known as
a transormative orcerdquo
Choices B C and D are incorrect because each misinterprets the relation-
ship between the proposed text and the passage
QUESTION 23
Choice A is the best answer It opens with a clause that identifies how
1-MCP affects apples which ocuses the sentence on 1-MCP as the subject
and allows the ideas in the sentence to progress logically
Choices B C and D are incorrect because each displays awkward or flawedmodification and progression o ideas or creates redundancy
QUESTION 24
Choice D is the best answer Only the comma is necessary to separate
ldquoethylenerdquo rom the appositive noun phrase that defines it
Choices A B and C are incorrect because each creates a comma splice and
or adds unnecessary words
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1940
18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040
19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140
20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240
21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340
22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440
23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640
25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940
28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040
29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3340
32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3540
34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640
35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 1940
18
QUESTION 25
Choice B is the best answer It offers an adjective that accurately describes
resh apples
Choices A C and D are incorrect because each proposes an adjective that
does not describe a plausible ruit texture
QUESTION 26
Choice A is the best answer Te plural possessive pronoun ldquotheirrdquo corre-
sponds with the plural reerent ldquoapplesrdquo
Choices B C and D are incorrect because none provides a pronoun that is
both possessive and plural
QUESTION 27
Choice D is the best answer It provides the pronoun ldquowhordquo which accu-rately identifies the reerent ldquoconsumersrdquo as people and appropriately begins
the relative clause
Choices A B and C are incorrect because each contains a pronoun that
either does not correspond with the human reerent ldquoconsumersrdquo or does
not correctly begin the relative clause
QUESTION 28
Choice B is the best answer It provides the present tense verb ldquodordquo which
corresponds to the present tense established earlier in the sentence
Choices A C and D are incorrect because each contains a verb that deviates
rom the simple present tense established in the sentence
QUESTION 29
Choice B is the best answer It provides a colon to appropriately introduce the
clause that ollows an elaboration on the preceding claim that Bartlett pears
are an example o ruit that ldquodo not respond as well to 1-MCP treatmentrdquo
Choices A C and D are incorrect because each either creates a commasplice or uses a transitional phrase (ldquoFor instancerdquo) illogically
QUESTION 30
Choice B is the best answer Sentence 4 begins with ldquoButrdquo indicating a con-
trast with a previous idea and goes on to mention that 1-MCP can have
negative effects Sentence 1 continues the discussion o benefits o 1-MCP
and sentence 2 names the adverse effect o limiting scent production so the
most logical spot or sentence 4 is between these sentences
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2040
19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2140
20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2240
21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340
22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440
23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640
25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940
28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040
29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3140
30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3340
32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3440
33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3540
34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640
35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740
36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3840
37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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19
Choices A C and D are incorrect because each proposes placing the sen-
tence at a point where it would compromise the logical development o ideas
in the paragraph
QUESTION 31
Choice D is the best answer It most accurately reflects the data in thegraph which shows a steep decrease in percentage o flesh browning when
untreated apples are lef in the open air or three weeks rather than placed
immediately into a controlled atmosphere
Choices A B and C are incorrect because each presents an inaccurate inter-
pretation o the data in the graph
QUESTION 32
Choice B is the best answer It accurately interprets the data as indicating
that ldquoroughly hal o their flesh turns brownrdquo when apples are treated with1-MCP both bars representing 1-MCP treatment are near the 50 line
Choices A C and D are incorrect because each proposes an inaccurate
interpretation o the data
QUESTION 33
Choice C is the best answer It describes an action weighing the relative
values that ruit sellers must take as a result o 1-MCPrsquos limitations
Choices A B and D are incorrect because none specifically connects the
shortcomings o 1-MCP with any action on the part o ruit sellers
QUESTION 34
Choice D is the best answer It clearly communicates that the preceding
dependent clause modifies ldquoworks by human artistsrdquo
Choices A B and C are incorrect because each ails to link the preced-
ing dependent clause to an independent clause resulting in an incomplete
sentence
QUESTION 35
Choice B is the best answer It provides the necessary em dash to close the
aside about artist CM Coolidge which opens with an em dash
Choices A C and D are incorrect because each provides closing punctua-
tion or the aside that does not correspond with the opening punctuation
QUESTION 36
Choice C is the best answer Te plural verb ldquoportrayrdquo corresponds with the
plural noun ldquoworks o artrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340
22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
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24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
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25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
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26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
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27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
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28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3540
34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640
35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740
36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3840
37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040
QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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20
Choices A B and D are incorrect because none provides the plural verb in
the present tense that the sentence requires
QUESTION 37
Choice D is the best answer It names a ldquomuseum in Russiardquo which is the
subject o the next paragraph
Choices A B and C are incorrect because each provides an overly general
phrase that does not specifically link to the paragraph that ollows
QUESTION 38
Choice C is the best answer It creates parallelism with the verb ldquocould
damagerdquo that appears earlier in the clause (ldquorodents that could damage
[and could] scare off visitorsrdquo)
Choices A B and D are incorrect because each presents a verb tense that is
inconsistent with the sentencersquos other present-tense verb (ldquocould damagerdquo)
that shares ldquomice rats and other rodentsrdquo as its subject
QUESTION 39
Choice C is the best answer Sentence 5 which discusses Peter the Greatrsquos
daughter continuing his tradition most logically ollows the sentence about
Peter the Great
Choices A B and D are incorrect because each presents a placement that
would compromise the logical development o the paragraph
QUESTION 40
Choice B is the best answer ldquoCommissionedrdquo describes the act o hiring an
artist to create a specific work
Choices A C and D are incorrect because each provides a word that does
not correspond logically with the context
QUESTION 41
Choice D is the best answer It provides punctuation that clearly places thenoun phrase ldquodigital artist Eldar Zakirovrdquo as an appositive identiying the per-
son mentioned in the previous phrase ldquoTe person chosen or this taskrdquo
Choices A B and C are incorrect because each ails to open and close the unin-
terrupted appositive noun phrase ldquodigital artist Eldar Zakirovrdquo with commas
QUESTION 42
Choice A is the best answer Te phrase ldquonoble individualsrdquo corresponds
with the subsequent examples o portraits where the cats are depicted as
ldquoaristocraticrdquo ldquostatelyrdquo and like a ldquotrusted royal advisorrdquo
7262019 PrepScholar Sat Practice Test 3 Answers
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21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2340
22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2440
23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640
25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2940
28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040
29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3840
37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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21
Choices B C and D are incorrect because each provides a statement that
does not logically connect to the examples that ollow
QUESTION 43
Choice D is the best answer It accurately states that the inormation in the
proposed additional sentence is not related to ormal portraits o cats themain topic o the paragraph
Choices A B and C are incorrect because each ails to recognize that the
proposed sentence interrupts the logical development o the paragraph
QUESTION 44
Choice D is the best answer Te tone corresponds with that established in
the passage and the phrasing appropriately ocuses on the catsrsquo contribution
to protecting artwork rather than on simply killing rodents
Choices A B and C are incorrect because none makes explicit the link
between the catsrsquo hunting activities and the service to the museum
Section 3 Math Test mdash No Calculator
QUESTION 1
Choice C is correct Te painterrsquos ee is given by nK ℓh where n is the number
o walls K is a constant with units o dollars per square oot ℓ is the length
o each wall in eet and h is the height o each wall in eet Examining this
equation shows that ℓ and h will be used to determine the area o each wall
Te variable n is the number o walls so n times the area o the walls will
give the amount o area that will need to be painted Te only remaining
variable is K which represents the cost per square oot and is determined by
the painterrsquos time and the price o paint Tereore K is the only actor that
will change i the customer asks or a more expensive brand o paint
Choice A is incorrect because a more expensive brand o paint would not
cause the height o each wall to change Choice B is incorrect because a more
expensive brand o paint would not cause the length o each wall to change
Choice D is incorrect because a more expensive brand o paint would notcause the number o walls to change
QUESTION 2
Choice D is correct Dividing each side o the equation 3r = 18 by 3 gives
r = 6 Substituting 6 or r in the expression 6r + 3 gives 6(6) + 3 = 39
Alternatively the expression 6r + 3 can be rewritten as 2(3r ) + 3 Substituting
18 or 3r in the expression 2(3r ) + 3 yields 2(18) + 3 = 36 + 3 = 39
7262019 PrepScholar Sat Practice Test 3 Answers
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22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
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24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
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25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
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26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
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27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
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28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040
29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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22
Choice A is incorrect because 6 is the value o r however the question asks
or the value o the expression 6r + 3 Choices B and C are incorrect because
i 6r + 3 were equal to either o these values then it would not be possible or
3r to be equal to 18 as stated in the question
QUESTION 3
Choice D is correct By definition a m
_ n = n radic _ am or any positive integers m
and n It ollows thereore that a2
_ 3
=
3 radic _
a2
Choice A is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to the
expression radic_
a 1
_ 3 yields radic
_
a1
_ 3
= ( a 1
_ 3
) 1
_ 2
= a
1 _
6 Because a
1 _
6 ne a
2 _
3 radic_
a 1
_ 3
is not the correct
answer Choice B is incorrect By definition a 1
_ n =n radic _
a or any positive integer n
Applying this definition as well as the power property o exponents to
the expression radic _
a 3 yields radic _
a 3 = (
a 3 ) 1 _ 2
= a
3 _ 2
Because a 3
_ 2
ne a 2
_ 3
radic _
a 3 is not the
correct answer Choice C is incorrect By definition a 1 _ n = n radic _
a or any positive
integer n Applying this definition as well as the power property o expo-
nents to the expression3
radic _
a 1 _ 2
yields
3
radic _
a 1 _ 2
= ( a 1 _ 2
) 1
_ 3
= a
1 _ 6
Because a
1 _ 6
ne a 2 _ 3
3
radic _
a 1 _ 2
is
not the correct answer
QUESTION 4
Choice B is correct o fit the scenario described 30 must be twice as large
as x Tis can be written as 2x = 30
Choices A C and D are incorrect Tese equations do not correctly relatethe numbers and variables described in the stem For example the expres-
sion in choice C states that 30 is hal as large as x not twice as large as x
QUESTION 5
Choice C is correct Multiplying each side o5
_ x
=15
_
x + 20 by x (x + 20) gives
15x = 5(x + 20) Distributing the 5 over the values within the parenthe-
ses yields 15x = 5x + 100 and then subtracting 5x rom each side gives
10x = 100 Finally dividing both sides by 10 gives x = 10 Tereore the value o
x _
5 is
10 _
5 = 2
Choice A is incorrect because it is the value o x notx
_ 5
Choices B and D
are incorrect and may be the result o errors in arithmetic operations on the
given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2540
24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
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25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
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27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
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28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
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23
QUESTION 6
Choice C is correct Multiplying each side o the equation 2x minus 3 y = minus14 by
3 gives 6x minus 9 y = minus42 Multiplying each side o the equation 3x minus 2 y = minus6 by
2 gives 6x minus 4 y = minus12 Ten subtracting the sides o 6x minus 4 y = minus12 rom the
corresponding sides o 6x minus 9 y = minus42 gives minus5 y = minus30 Dividing each side
o the equation minus5 y = minus30 by minus5 gives y = 6 Finally substituting 6 or y in2x minus 3 y = minus14 gives 2x minus 3(6) = minus14 or x = 2 Tereore the value o x minus y is
2 minus 6 = minus4
Alternatively adding the corresponding sides o 2x minus 3 y = minus14 and
3x minus 2 y = minus6 gives 5x minus 5 y = minus20 rom which it ollows that x minus y = minus4
Choices A B and D are incorrect and may be the result o an arithmetic
error when solving the system o equations
QUESTION 7
Choice C is correct I x minus b is a actor o f (x ) then f (b) must equal 0 Based
on the table f (4) = 0 Tereore x minus 4 must be a actor o f (x )
Choice A is incorrect because f (2) ne 0 choice B is incorrect because no
inormation is given about the value o f (3) so x minus 3 may or may not be a
actor o f (x ) and choice D is incorrect because f (5) ne 0
QUESTION 8
Choice A is correct Te linear equation y = kx + 4 is in slope-intercept orm
and so the slope o the line is k Since the line contains the point (c d ) the
coordinates o this point satisy the equation y = kx + 4 d = kc + 4 Solving
this equation or the slope k gives k =d minus 4_
c
Choices B C and D are incorrect and may be the result o errors in substi-
tuting the coordinates o (c d ) in y = kx + 4 or o errors in solving or k in
the resulting equation
QUESTION 9
Choice A is correct I a system o two linear equations has no solution then
the lines represented by the equations in the coordinate plane are parallel
Te equation kx minus 3 y = 4 can be rewritten as y = k _ 3
x minus 4 _ 3
where k _ 3
is the slope
o the line and the equation 4x minus 5 y = 7 can be rewritten as y =4
_ 5
x minus7
_ 5
where4
_ 5
is the slope o the line I two lines are parallel then the slopes o
the line are equal Tereore4
_ 5
=k
_ 3
or k =12 _
5 (Since the y -intercepts o the
lines represented by the equations are minus4
_ 3
and minus7
_ 5
the lines are parallel not
identical)
Choices B C and D are incorrect and may be the result o a computational
error when rewriting the equations or solving the equation representing the
equality o the slopes or k
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24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
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25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
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26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
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27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
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28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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24
QUESTION 10
Choice A is correct Substituting 25 or y in the equation y = (x minus 11)2 gives
25 = (x minus 11)2 It ollows that x minus 11 = 5 or x minus 11 = minus5 so the x -coordinates
o the two points o intersection are x = 16 and x = 6 respectively Since
both points o intersection have a y -coordinate o 25 it ollows that the two
points are (16 25) and (6 25) Since these points lie on the horizontal line y = 25 the distance between these points is the positive difference o the
x -coordinates 16 minus 6 = 10
Choices B C and D are incorrect and may be the result o an error in solv-
ing the quadratic equation that results when substituting 25 or y in the
given quadratic equation
QUESTION 11
Choice B is correct Since the angles marked y deg and udeg are vertical angles
y = u Subtracting the sides o y = u rom the corresponding sides o x + y = u + w gives x = w Since the angles marked wdeg and z deg are vertical angles
w = z Tereore x = z and so I must be true
Te equation in II need not be true For example i x = w = z = t = 70 and
y = u = 40 then all three pairs o vertical angles in the figure have equal
measure and the given condition x + y = u + w holds But it is not true in this
case that y is equal to w Tereore II need not be true
Since the top three angles in the figure orm a straight angle it ollows that
x + y + z = 180 Similarly w + u + t = 180 and so x + y + z = w + u + t
Subtracting the sides o the given equation x + y = u + w rom the corre-
sponding sides o x + y + z = w + u + t gives z = t Tereore III must be true
Since only I and III must be true the correct answer is choice B
Choices A C and D are incorrect because each o these choices includes II
which need not be true
QUESTION 12
Choice A is correct Te parabola with equation y = a(x minus 2)(x + 4) crosses
the x -axis at the points (minus4 0) and (2 0) Te x -coordinate o the vertex
o the parabola is halway between the x -coordinates o (minus4 0) and (2 0)
Tus the x -coordinate o the vertex isminus4 + 2
_
2 = minus1 Tis is the value o c o
find the y -coordinate o the vertex substitute minus1 or x in y = a(x minus 2)(x + 4)
y = a(x minus 2)(x + 4) = a(minus1 minus 2)(minus1 + 4) = a(minus3)(3) = minus9a
Tereore the value o d is minus9a
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2640
25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2740
26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 2840
27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
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28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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25
Choice B is incorrect because the value o the constant term in the equa-
tion is not the y -coordinate o the vertex unless there were no linear terms
in the quadratic Choice C is incorrect and may be the result o a sign error
in finding the x -coordinate o the vertex Choice D is incorrect because
the negative o the coefficient o the linear term in the quadratic is not the
y -coordinate o the vertex
QUESTION 13
Choice B is correct Since 24x 2 + 25x minus 47 divided by ax minus 2 is equal to
minus8x minus3 with remainder minus53 it is true that (minus8x minus 3)(ax minus 2) minus 53 = 24x 2 +
25x minus47 (Tis can be seen by multiplying each side o the given equation by
ax minus 2) Tis can be rewritten as minus8ax 2 + 16x minus 3ax = 24x 2 + 25x minus 47 Since
the coefficients o the x 2-term have to be equal on both sides o the equation
minus8a = 24 or a = minus3
Choices A C and D are incorrect and may be the result o either a concep-tual misunderstanding or a computational error when trying to solve or the
value o a
QUESTION 14
Choice A is correct Dividing each side o the given equation by 3 gives
the equivalent equation x 2 + 4x + 2 = 0 Ten using the quadratic ormula
minusb plusmn radic _
b 2 minus 4ac__
2a with a = 1 b = 4 and c = 2 gives the solutions x = minus2 plusmn radic
_ 2
Choices B C and D are incorrect and may be the result o errors when
applying the quadratic ormula
QUESTION 15
Choice D is correct I C is graphed against F the slope o the graph is equal
to5
_ 9
degrees Celsiusdegrees Fahrenheit which means that or an increase o
1 degree Fahrenheit the increase is5
_ 9
o 1 degree Celsius Tus statement I
is true Tis is the equivalent to saying that an increase o 1 degree Celsius
is equal to an increase o9
_ 5
degrees Fahrenheit Since9
_ 5
= 18 statement II
is true On the other hand statement III is not true since a temperature
increase o9
_ 5
degrees Fahrenheit not5
_ 9
degree Fahrenheit is equal to a tem-
perature increase o 1 degree Celsius
Choices A B and C are incorrect because each o these choices omits a true
statement or includes a alse statement
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26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
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27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
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28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640
35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740
36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3840
37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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26
QUESTION 16
The correct answer is either 1 or 2 Te given equation can be rewritten as
x 5 minus 5x 3 + 4x = 0 Since the polynomial expression on the lef has no constant
term it has x as a actor x (x 4 minus 5x 2 + 4) = 0 Te expression in parentheses is
a quadratic equation in x 2 that can be actored giving x (x 2 minus 1)(x 2 minus 4) = 0
Tis urther actors as x (x minus 1)(x + 1)(x minus 2)(x + 2) = 0 Te solutions orx are x = 0 x = 1 x = minus1 x = 2 and x = minus2 Since it is given that x gt 0 the
possible values o x are x = 1 and x = 2 Either 1 or 2 may be gridded as the
correct answer
QUESTION 17
The correct answer is 2 First clear the ractions rom the given equation by
multiplying each side o the equation by 36 (the least common multiple o 4
9 and 12) Te equation becomes 28x minus 16x = 9 + 15 Combining like terms
on each side o the equation yields 12x = 24 Finally dividing both sides o
the equation by 12 yields x = 2
Alternatively since7
_ 9
x minus4
_ 9
x =3
_ 9
x =1
_ 3
x and1
_ 4
+5
_
12 =
3 _
12 +
5 _
12 =
8 _
12 =
2 _
3 the
given equation simplifies to1
_ 3
x =2
_ 3
Multiplying each side o1
_ 3
x =2
_ 3
by 3
yields x = 2
QUESTION 18
The correct answer is 105 Since 180 minus z = 2 y and y = 75 it ollows that
180 minus z = 150 and so z = 30 Tus each o the base angles o the isosceles
triangle on the right has measure180deg minus 30deg
_
2 = 75deg Tereore the measure o
the angle marked x deg is 180deg minus 75deg = 105deg and so the value o x is 105
QUESTION 19
The correct answer is 370 A system o equations can be used where h rep-
resents the number o calories in a hamburger and f represents the number
o calories in an order o ries Te equation 2h + 3 f = 1700 represents the
act that 2 hamburgers and 3 orders o ries contain a total o 1700 calories
and the equation h = f + 50 represents the act that one hamburger contains
50 more calories than an order o ries Substituting f + 50 or h in 2h + 3 f =
1700 gives 2( f + 50) + 3 f = 1700 Tis equation can be solved as ollows
2 f + 100 + 3 f = 1700
5 f + 100 = 1700
5 f = 1600
f = 320
Te number o calories in an order o ries is 320 so the number o calories
in a hamburger is 50 more than 320 or 370
7262019 PrepScholar Sat Practice Test 3 Answers
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27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
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28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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27
QUESTION 20
The correct answer is3
_ 5
or 6 riangle ABC is a right triangle with its right
angle at B Tus_
AC is the hypotenuse o right triangle ABC and_
AB and_
BC are the legs o right triangle ABC By the Pythagorean theorem AB =
radic
_
202
minus 162
= radic
_
400 minus 256 = radic
_
144 = 12 Since triangle DEF is similar to tri-angle ABC with vertex F corresponding to vertex C the measure o angle
F equals the measure o angle C Tus sinF = sinC From the side lengths
o triangle ABC sinC =opposite side
_
hypotenuse =
AB
_
AC =
12 _
20 =
3 _
5 Tereore sinF =
3 _
5
Either3
_ 5
or its decimal equivalent 6 may be gridded as the correct answer
Section 4 Math Test ndash Calculator
QUESTION 1
Choice C is correct Marilynrsquos distance rom her campsite remained the same
during the time she ate lunch Tis is represented by a horizontal segment in
the graph Te only horizontal segment in the graph starts at a time o about
110 983152983149 and ends at about 140 983152983149 Tereore Marilyn finished her lunch
and continued her hike at about 140 983152983149
Choices A B and D are incorrect and may be the result o a misinterpre-
tation o the graph For example choice B is the time Marilyn started her
lunch and choice D is the time Marilyn was at the maximum distance rom
her campsite
QUESTION 2
Choice B is correct O the 25 people who entered the contest there are
8 emales under age 40 and 2 males age 40 or older Tereore the probabil-
ity that the contest winner will be either a emale under age 40 or a male age
40 or older is8
_
25 +
2 _
25 =
10 _
25
Choice A is incorrect and may be the result o dividing 8 by 2 instead o
adding 8 to 2 to find the probability Choice C is incorrect it is the probabil-
ity that the contest winner will be either a emale under age 40 or a emaleage 40 or older Choice D is incorrect and may be the result o multiplying 8
and 2 instead o adding 8 and 2 to find the probability
QUESTION 3
Choice C is correct Based on the graph sales increased in the first 3 years
since 1997 which is until year 2000 and then generally decreased thereafer
Choices A B and D are incorrect each o these choices contains inaccura-
cies in describing the general trend o music album sales rom 1997 to 2000
7262019 PrepScholar Sat Practice Test 3 Answers
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28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3040
29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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28
QUESTION 4
Choice C is correct Te graph o y = f (n) in the coordinate plane is a line
that passes through each o the points given in the table From the table one
can see that an increase o 1 unit in n results in an increase o 3 units in f (n)
or example f (2) minus f (1) = 1 minus (minus2) = 3 Tereore the graph o y = f (n) in the
coordinate plane is a line with slope 3 Only choice C is a line with slope 3Te y -intercept o the line is the value o f (0) Since an increase o 1 unit in
n results in an increase o 3 units in f (n) it ollows that f (1) minus f (0) = 3 Since
f (1) = minus2 it ollows that f (0) = f (1) minus 3 = minus5 Tereore the y -intercept o the
graph o f (n) is minus5 and the slope-intercept equation or f (n) is f (n) = 3n minus 5
Choices A B and D are incorrect because each equation has the incorrect
slope o the line (the y -intercept in each equation is also incorrect)
QUESTION 5
Choice B is correct Since 7 percent o the 562 juniors is 007(562) and 5 percento the 602 seniors is 005(602) the expression 007(562) + 005(602) can be eval-
uated to determine the total number o juniors and seniors inducted into the
honor society O the given choices 69 is closest to the value o the expression
Choice A is incorrect and may be the result o adding the number o juniors
and seniors and the percentages given and then using the expression
(007 + 005)(562 + 602) Choices C and D are incorrect and may be the
result o finding either only the number o juniors inducted or only the
number o seniors inducted
QUESTION 6
Choice A is correct Te sum o the two polynomials is ( 3x 2 minus 5x + 2 ) +
( 5x 2 minus 2x minus 6) Tis can be rewritten by combining like terms
(
3x 2 minus 5x + 2) + ( 5x 2 minus 2x minus 6) = (
3x 2 + 5x 2 ) + (
minus5x minus 2x) + ( 2 minus 6 ) = 8x 2 minus 7x minus 4
Choice B is incorrect and may be the result o a sign error when combining
the coefficients o the x-term Choice C is incorrect and may be the result o
adding the exponents as well as the coefficients o like terms Choice D is
incorrect and may be the result o a combination o the errors described in
B and C
QUESTION 7
Choice D is correct o solve the equation or w multiply both sides o the
equation by the reciprocal o3
_ 5
which is5
_ 3
Tis gives ( 5 _ 3
) middot3
_ 5
w =4
_ 5
middot ( 5
_ 3
) which simplifies to w =
20 _
9
Choices A B and C are incorrect and may be the result o errors in arithme-
tic when simpliying the given equation
7262019 PrepScholar Sat Practice Test 3 Answers
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29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640
35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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29
QUESTION 8
Choice C is correct In the equation y = 056x + 272 the value o x increases
by 1 or each year that passes Each time x increases by 1 y increases by
056 since 056 is the slope o the graph o this equation Since y represents
the average number o students per classroom in the year represented by
x it ollows that according to the model the estimated increase each yearin the average number o students per classroom at Central High School
is 056
Choice A is incorrect because the total number o students in the school in
2000 is the product o the average number o students per classroom and
the total number o classrooms which would appropriately be approximated
by the y -intercept (272) times the total number o classrooms which is not
given Choice B is incorrect because the average number o students per
classroom in 2000 is given by the y -intercept o the graph o the equation
but the question is asking or the meaning o the number 056 which is theslope Choice D is incorrect because 056 represents the estimated yearly
change in the average number o students per classroom Te estimated di-
erence between the average number o students per classroom in 2010 and
2000 is 056 times the number o years that have passed between 2000 and
2010 that is 056 times 10 = 56
QUESTION 9
Choice B is correct Because Nate walks 25 meters in 137 seconds and
4 minutes is equal to 240 seconds the proportion
25 meters
_
137 sec =
x meters_
240 sec can be used to find out how many meters x Nate walks in 4 minutes Te
proportion can be simplified to25
_
137 =
x
_
240 because the units o meters per
second cancel and then each side o the equation can be multiplied by 240
giving(240)(25)
_
137 = x asymp 438 Tereore o the given options 450 meters is
closest to the distance Nate will walk in 4 minutes
Choice A is incorrect and may be the result o setting up the proportion
as137 sec
_
25 meters
=x meters
_
240 sec
and finding that x asymp 132 which is close to 150
Choices C and D are incorrect and may be the result o errors in calculation
QUESTION 10
Choice D is correct On Mercury the acceleration due to gravity is
36 msec2 Substituting 36 or g and 90 or m in the ormula W = mg gives
W = 90(36) = 324 newtons
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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30
Choice A is incorrect and may be the result o dividing 90 by 36 Choice B
is incorrect and may be the result o subtracting 36 rom 90 and rounding
to the nearest whole number Choice C is incorrect because an object with
a weight o 101 newtons on Mercury would have a mass o about 28 kilo-
grams not 90 kilograms
QUESTION 11
Choice B is correct On Earth the acceleration due to gravity is 98 msec 2
Tus or an object with a weight o 150 newtons the ormula W = mg
becomes 150 = m(98) which shows that the mass o an object with a weight
o 150 newtons on Earth is about 153 kilograms Substituting this mass
into the ormula W = mg and now using the weight o 170 newtons gives
170 = 153 g which shows that the second planetrsquos acceleration due to gravity
is about 111 msec2 According to the table this value or the acceleration
due to gravity holds on Saturn
Choices A C and D are incorrect Using the ormula W = mg and the values
or g in the table shows that an object with a weight o 170 newtons on these
planets would not have the same mass as an object with a weight o 150 new-
tons on Earth
QUESTION 12
Choice D is correct A zero o a unction corresponds to an x -intercept o
the graph o the unction in the xy -plane Tereore the complete graph
o the unction f which has five distinct zeros must have five x -intercepts
Only the graph in choice D has five x -intercepts and thereore this is theonly one o the given graphs that could be the complete graph o f in the
xy -plane
Choices A B and C are incorrect Te number o x -intercepts o each o
these graphs is not equal to five thereore none o these graphs could be the
complete graph o f which has five distinct zeros
QUESTION 13
Choice D is correct Starting with the original equation h = minus 16t 2 + vt + k
in order to get v in terms o the other variables minus16t 2 and k need to be
subtracted rom each side Tis yields vt = h + 16t 2 minus k which when
divided by t will give v in terms o the other variables However the equa-
tion v =h + 16t2 minus k
_
t is not one o the options so the right side needs to
be urther simplified Another way to write the previous equation is
v =h minus k
_
t +
16t 2 _
t which can be simplified to v =
h minus k
_
t + 16t
Choices A B and C are incorrect and may be the result o arithmetic errors
when rewriting the original equation to express v in terms o h t and k
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3440
33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3540
34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640
35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740
36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3840
37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3940
38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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31
QUESTION 14
Choice A is correct Te hotel charges $020 per minute to use the meeting-
room phone Tis per-minute rate can be converted to the hourly rate using
the conversion 1 hour = 60 minutes as shown below
$020
_
minute times
60 minutes
_
1 hour=
$(020 times 60)_
hour
Tus the hotel charges $(020 times 60) per hour to use the meeting-room
phone Tereore the cost c in dollars or h hours o use is c = (020 times 60)h
which is equivalent to c = 020(60h)
Choice B is incorrect because in this expression the per-minute rate is mul-
tiplied by h the number o hours o phone use Furthermore the equation
indicates that there is a flat ee o $60 in addition to the per-minute or per-
hour rate Tis is not the case Choice C is incorrect because the expression
indicates that the hotel charges $( 60
_
020 ) per hour or use o the meeting-
room phone not $020(60) per hour Choice D is incorrect because the
expression indicates that the hourly rate is1
_
60 times the per-minute rate not
60 times the per-minute rate
QUESTION 15
Choice A is the correct answer Experimental research is a method used
to study a small group o people and generalize the results to a larger
population However in order to make a generalization involving cause
and eect
Te population must be well defined
Te participants must be selected at random
Te participants must be randomly assigned to treatment groups
When these conditions are met the results o the study can be generalized
to the population with a conclusion about cause and effect In this study
all conditions are met and the population rom which the participants were
selected are people with poor eyesight Tereore a general conclusion can
be drawn about the effect o reatment X on the population o people with
poor eyesight
Choice B is incorrect Te study did not include all available treatments
so no conclusion can be made about the relative effectiveness o all avail-
able treatments Choice C is incorrect Te participants were selected at
random rom a large population o people with poor eyesight Tereore
the results can be generalized only to that population and not to anyone in
general Also the conclusion is too strong an experimental study might
show that people are likely to be helped by a treatment but it cannot show
that anyone who takes the treatment will be helped Choice D is incorrect
7262019 PrepScholar Sat Practice Test 3 Answers
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
7262019 PrepScholar Sat Practice Test 3 Answers
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640
35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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32
Tis conclusion is too strong Te study shows that reatment X is likely to
improve the eyesight o people with poor eyesight but it cannot show that
the treatment definitely will cause improvement in eyesight or every per-
son Furthermore since the people undergoing the treatment in the study
were selected rom people with poor eyesight the results can be generalized
only to this population not to all people
QUESTION 16
Choice B is correct For any value o x say x = x 0 the point (x
0 f (x
0)) lies
on the graph of f and the point (x 0 g (x
0)) lies on the graph of g hus or
any value o x say x = x 0 the value of f (x
0) + g (x
0) is equal to the sum of the
y -coordinates o the points on the graphs o f and g with x -coordinate equal
to x 0 Therefore the value of x or which f (x ) + g (x ) is equal to 0 will occur
when the y -coordinates o the points representing f (x ) and g (x ) at the same
value o x are equidistant rom the x -axis and are on opposite sides o the
x -axis Looking at the graphs one can see that this occurs at x = minus2 thepoint (minus2 minus2) lies on the graph o f and the point (minus2 2) lies on the graph o
g Tus at x = minus2 the value o f (x ) + g (x ) is minus2 + 2 = 0
Choices A C and D are incorrect because none o these x -values satisy the
given equation f (x ) + g (x ) = 0
QUESTION 17
Choice B is correct Te quantity o the product supplied to the market is
given by the unction S(P ) =1
_
2
P + 40 I the price P o the product increases
by $10 the effect on the quantity o the product supplied can be determined
by substituting P + 10 or P as the argument in the unction his gives
S(P + 10) =1
_ 2
(P + 10) + 40 =1
_ 2
P + 45 which shows that S(P + 10) = S(P ) + 5
hereore the quantity supplied to the market will increase by 5 units when
the price o the product is increased by $10
Alternatively look at the coefficient o P in the linear unction S his is the
slope o the graph o the unction where P is on the horizontal axis and S(P )
is on the vertical axis Since the slope is1
_ 2
or every increase o 1 in P there
will be an increase o 1 _ 2 in S(P ) and thereore an increase o 10 in P will
yield an increase o 5 in S(P )
Choice A is incorrect I the quantity supplied decreases as the price o the
product increases the unction S(P ) would be decreasing but S(P ) =1
_ 2
P + 40 is
an increasing unction Choice C is incorrect and may be the result o assum-
ing the slope o the graph o S(P ) is equal to 1 Choice D is incorrect and may
be the result o conusing the y -intercept o the graph o S(P ) with the slope
and then adding 10 to the y -intercept
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33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3440
33
QUESTION 18
Choice B is correct he quantity o the product supplied to the market will
equal the quantity o the product demanded by the market i S(P ) is equal to
D(P ) that is i1
_ 2
P + 40 = 220 minus P Solving this equation gives P = 120 and
so $120 is the price at which the quantity o the product supplied will equalthe quantity o the product demanded
Choices A C and D are incorrect At these dollar amounts the quantities
given by S(P ) and D(P ) are not equal
QUESTION 19
Choice C is correct It is given that 1 ounce o graphene covers 7 ootball
fields Tereore 48 ounces can cover 7 times 48 = 336 ootball fields I each
ootball field has an area o 11
_
3
acres than 336 ootball fields have a total area
o 336 times 11 _ 3
= 448 acres Tereore o the choices given 450 acres is closest
to the number o acres 48 ounces o graphene could cover
Choice A is incorrect and may be the result o dividing instead o multiply-
ing the number o ootball fields by 11
_ 3
Choice B is incorrect and may be
the result o finding the number o ootball fields not the number o acres
that can be covered by 48 ounces o graphene Choice D is incorrect and
may be the result o setting up the expression7 times 48 times 4
_
3 and then finding
only the numerator o the raction
QUESTION 20
Choice B is correct o answer this question find the point in the graph
that represents Michaelrsquos 34-minute swim and then compare the actual
heart rate or that swim with the expected heart rate as defined by the line
o best fit o find the point that represents Michaelrsquos swim that took 34
minutes look along the vertical line o the graph that is marked ldquo34rdquo on
the horizontal axis hat vertical line intersects only one point in the scat-
terplot at 148 beats per minute On the other hand the line o best fit
intersects the vertical line representing 34 minutes at 150 beats per min-ute Tereore or the swim that took 34 minutes Michaelrsquos actual heart
rate was 150 minus 148 = 2 beats per minute less than predicted by the line o
best fit
Choices A C and D are incorrect and may be the result o misreading the
scale o the graph
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640
35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740
36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3840
37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3940
38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040
QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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34
QUESTION 21
Choice C is correct Let I be the initial savings I each successive year 1 o the
current value is added to the value o the account then afer 1 year the amount
in the account will be I + 001I = I (1 + 001) afer 2 years the amount in the
account will be I (1 + 001) + 001I (1 + 001) = (1 + 001)I (1 + 001) = I (1 + 001)2
and afer t years the amount in the account will be I (1 + 001)t Tis is exponen-tial growth o the money in the account
Choice A is incorrect I each successive year 2 o the initial savings I
is added to the value o the account then afer t years the amount in the
account will be I + 002It which is linear growth Choice B is incorrect
I each successive year 15 o the initial savings I and $100 is added to
the value o the the account then afer t years the amount in the account
will be I + (0015I + 100)t which is linear growth Choice D is incorrect
I each successive year $100 is added to the value o the account then
afer t years the amount in the account will be I + 100t which is lineargrowth
QUESTION 22
Choice B is correct One o the three numbers is x let the other two numbers
be y and z Since the sum o three numbers is 855 the equation x + y + z = 855
is true Te statement that x is 50 more than the sum o the other two
numbers can be represented as x = 15( y + z ) orx
_
15 = y + z Substituting
x
_
15
or y + z in x + y + z = 855 gives x +x
_
15 = 855 his last equation can be
rewritten as x + 2x
_
3
= 855 or 5x
_
3
= 855 Tereore x equals 3 _ 5
times 855 = 513
Choices A C and D are incorrect and may be the result o calculation errors
QUESTION 23
Choice C is correct Since the angles are acute and sin(adeg) = cos(bdeg) it ollows
rom the complementary angle property o sines and cosines that a + b = 90
Substituting 4k minus 22 or a and 6k minus 13 or b gives (4k minus 22) + (6k minus 13) = 90
which simplifies to 10k minus 35 = 90 Tereore 10k = 125 and k = 125
Choice A is incorrect and may be the result o mistakenly assuming that
a + b and making a sign error Choices B and D are incorrect because they
result in values or a and b such that sin(adeg) ne cos(bdeg)
QUESTION 24
Choice D is correct Let c be the number o students in Mr Kohlrsquos class Te
conditions described in the question can be represented by the equations
n = 3c + 5 and n + 21 = 4c Substituting 3c + 5 or n in the second equation
gives 3c + 5 + 21 = 4c which can be solved to find c = 26
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3640
35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3740
36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3840
37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 3940
38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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35
Choices A B and C are incorrect because the values given for the number of
students in the class cannot fulfill both conditions given in the question For
example if there were 16 students in the class then the first condition would
imply that there are 3(16) + 5 = 53 milliliters of solution in the beaker but
the second condition would imply that there are 4(16) minus 21 = 43 milliliters of
solution in the beaker Tis contradiction shows that there cannot be 16 stu-dents in the class
QUESTION 25
Choice A is incorrect because this is the volume of only the two cones
Choice B is incorrect because this is the volume of only the cylinder Choice
C is incorrect because this is the volume of only one of the cones plus the
cylinder
QUESTION 26
Choice C is correct Te line passes through the origin (2 k) and (k 32)Any two of these points can be used to find the slope of the line Since the
line passes through (0 0) and (2 k) the slope of the line is equal tok minus 0
_
2 minus 0 =
k _
2
Similarly since the line passes through (0 0) and (k 32) the slope of the line
is equal to32 minus 0
_
k minus 0 =
32
_
k Since each expression gives the slope of the same line
it must be true thatk _
2 =
32
_
k Multiplying each side of
k _
2 =
32
_
k by 2k gives k2 = 64
from which it follows that k = 8 or k = minus8 Terefore of the given choices only
8 could be the value of k
Choices A B and D are incorrect and may be the result of calculation errors
QUESTION 27
Choice C is correct Let and w be the length and width respectively of the
original rectangle Te area of the original rectangle is A =w Te rectangle
is altered by increasing its length by 10 percent and decreasing its width by
p percent thus the length of the altered rectangle is 11 and the width of
the altered rectangle is ( 1 minus p
_
100 ) w Te alterations decrease the area by
12 percent so the area of the altered rectangle is (1 minus 012) A = 088 A
Choice D is correct The volume of the grain silo can be found by adding
the volumes of all the solids of which it is composed The silo is made up
of a cylinder with height 10 feet (ft) and base radius 5 feet and two cones
each having height 5 ft and base radius 5 ft The formulas V cylinder = r 2h and
V cone =1
3 r 2h can be used to determine the total volume of the silo Since
the two cones have identical dimensions the total volume in cubic feet of
the silo is given by V silo = (5)2(10) + (2) 13
(5)2(5) =43 (250) which is
approximately equal to 10472 cubic feet
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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36
Te altered rectangle is the product o its length and width so 088 A =
(11)( 1 minus p _
100 ) w Since A = w this last equation can be rewritten as
088 A = (11)( 1 minusP _
100 ) w = (11)( 1 minus
P
_
100 ) A rom which it ollows that
088 = (11)
( 1 minus
P
_
100
) or 08 =
( 1 minus P
_
100
) Tereore
P
_
100 = 02 and so the
value o p is 20
Choice A is incorrect and may be the result o conusing the 12 percent
decrease in area with the percent decrease in width Choice B is incorrect
because decreasing the width by 15 percent results in a 65 percent decrease
in area not a 12 percent decrease Choice D is incorrect and may be the
result o adding the percents given in the question (10 + 12)
QUESTION 28
Choice D is correct For the present population to decrease by 10 percentit must be multiplied by the actor 09 Since the engineer estimates that the
population will decrease by 10 percent every 20 years the present popula-
tion 50000 must be multiplied by (09)n where n is the number o 20-year
periods that will have elapsed t years rom now Afer t years the number o
20-year periods that have elapsed ist _
20 Tereore 50000(09)
t _
20 represents
the engineerrsquos estimate o the population o the city t years rom now
Choices A B and C are incorrect because each o these choices either con-
uses the percent decrease with the multiplicative actor that represents the
percent decrease or mistakenly multiplies t by 20 to find the number o
20-year periods that will have elapsed in t years
QUESTION 29
Choice A is correct Let x be the number o lef-handed emale students and
let y be the number o lef-handed male students Ten the number o right-
handed emale students will be 5x and the number o right-handed male
students will be 9 y Since the total number o lef-handed students is 18 and
the total number o right-handed students is 122 the system o equations
below must be satisfied
983093 x + y = 18
5x + 9 y = 122
Solving this system gives x = 10 and y = 8 Tus 50 o the 122 right-handed
students are emale Tereore the probability that a right-handed student
selected at random is emale is50
_
122 which to the nearest thousandth is 0410
Choices B C and D are incorrect and may be the result o incorrect calcula-
tion o the missing values in the table
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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37
QUESTION 30
Choice A is correct Subtracting the sides o 3 y + c = 5 y minus 7 rom the corre-
sponding sides o 3x + b = 5x minus 7 gives (3x minus 3 y ) + (b minus c) = (5x minus 5 y ) Since
b = c minus1
_ 2
or b minus c = minus1
_ 2
it ollows that (3x minus 3 y ) + ( minus1 _
2 ) = (5x minus 5 y ) Solving
this equation or x in terms o y gives x = y minus
1
_ 4 Tereore x is y minus
1
_ 4
Choices B C and D are incorrect and may be the result o making a compu-
tational error when solving the equations or x in terms o y
QUESTION 31
The correct answer is either 4 or 5 Because each student ticket costs $2 and
each adult ticket costs $3 the total amount in dollars that Chris spends on
x student tickets and 1 adult ticket is 2(x ) + 3(1) Because Chris spends at
least $11 but no more than $14 on the tickets one can write the compound
inequality 2x + 3 ge 11 and 2x + 3 le 14 Subtracting 3 rom each side o bothinequalities and then dividing each side o both inequalities by 2 yields x ge 4
and x le 55 Tus the value o x must be an integer that is both greater than
or equal to 4 and less than or equal to 55 Tereore x = 4 or x = 5 Either 4
or 5 may be gridded as the correct answer
QUESTION 32
The correct answer is 586 Te mean o a data set is determined by calculating
the sum o the values and dividing by the number o values in the data set Te
sum o the ages in years in the data set is 703 and the number o values in the
data set is 12 Tus the mean o the ages in years o the first 12 United States
presidents at the beginning o their terms is703
_
12 Te raction
703
_
12 cannot be
entered into the grid so the decimal equivalent rounded to the nearest tenth
is the correct answer Tis rounded decimal equivalent is 586
QUESTION 33
The correct answer is 9 o rewrite the difference (minus3x2 + 5x minus 2) minus 2(x2 minus 2x minus 1)
in the orm ax2 +bx +c the expression can be simplified by using the distributive
property and combining like terms as ollows
(minus3x2 + 5x minus 2) minus (2x2 minus 4x minus 2)
(minus3x2 minus 2x2 ) + (5x minus (minus4x )) + (minus2 minus(minus2))
minus5x2 + 9x + 0
Te coefficient o x is the value o b which is 9
Alternatively since b is the coefficient o x in the difference (minus3x2 + 5x minus 2) minus
2(x2 minus 2x minus 1) one need only compute the x -term in the difference Te x -term
is 5x minus 2(minus2x ) = 5x + 4x = 9x so the value o b is 9
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
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QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
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38
QUESTION 34
The correct answer is5
_ 8
or 625 A complete rotation around a point is 360deg
or 2π radians Since the central angle AOB has measure5π
_ 4
radians it rep-
resents
5π
_ 4
_
2π
=5
_
8
o a complete rotation around point O Tereore the sector
ormed by central angle AOB has area equal to 5 _ 8
the area o the entire circle
Either the raction5
_ 8
or its decimal equivalent 625 may be gridded as the
correct answer
QUESTION 35
The correct answer is 50 Te mean o a data set is the sum o the values
in the data set divided by the number o values in the data set Te mean o
75 is obtained by finding the sum o the first 10 ratings and dividing by 10
Tus the sum o the first 10 ratings was 750 In order or the mean o the
first 20 ratings to be at least 85 the sum o the first 20 ratings must be at least
(85)(20) = 1700 Tereore the sum o the next 10 ratings must be at least
1700 minus 750 = 950 Te maximum rating is 100 so the maximum possible
value o the sum o the 12th through 20th ratings is 9 times 100 = 900 Tereore
or the store to be able to have an average o at least 85 or the first 20 ratings
the least possible value or the 11th rating is 950 minus 900 = 50
QUESTION 36
The correct answer is 750 Te inequalities y le minus15x + 3000 and y le 5x
can be graphed in the xy -plane Tey are represented by the hal-planesbelow and include the boundary lines y = minus15x + 3000 and y = 5x respec-
tively Te solution set o the system o inequalities will be the intersection
o these hal-planes including the boundary lines and the solution (a b)
with the greatest possible value o b will be the point o intersection o the
boundary lines Te intersection o boundary lines o these inequalities can
be ound by setting them equal to each other 5x = minus15x + 3000 which has
solution x = 150 Tus the x-coordinate o the point o intersection is 150
Tereore the y -coordinate o the point o intersection o the boundary lines
is 5(150) = minus15(150) + 3000 = 750 Tis is the maximum possible value o b
or a point (a b) that is in the solution set o the system o inequalities
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040
QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time
7262019 PrepScholar Sat Practice Test 3 Answers
httpslidepdfcomreaderfullprepscholar-sat-practice-test-3-answers 4040
QUESTION 37
The correct answer is 7 Te average number o shoppers N in the check-
out line at any time is N = rt where r is the number o shoppers entering
the checkout line per minute and T is the average number o minutes each
shopper spends in the checkout line Since 84 shoppers per hour make a
purchase 84 shoppers per hour enter the checkout line Tis needs to beconverted to the number o shoppers per minute Since there are 60 minutes
in one hour the rate is84 shoppers
_
60 minutes = 14 shoppers per minute Using the
given ormula with r = 14 and t = 5 yields N = rt = (14)(5) = 7 Tereore
the average number o shoppers N in the checkout line at any time during
business hours is 7
QUESTION 38
The correct answer is 60 Te estimated average number o shoppers in the
original store at any time is 45 In the new store the manager estimates that
an average o 90 shoppers per hour enter the store which is equivalent to
15 shoppers per minute Te manager also estimates that each shopper stays
in the store or an average o 12 minutes Tus by Littlersquos law there are on
average N = rt = (15)(12) = 18 shoppers in the new store at any time Tis
is45 minus 18
_
45 times 100 = 60 percent less than the average number o shoppers in
the original store at any time