1991 State Countdown Round

8/20/2019 1991 State Countdown Round

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MATHCOUNTS

1990-1991

State Countdown Round



How many of the even counting

numbers less than 100 areprime?



nswer! 1



"he probability of rain on anygiven day in tlanta is #0$%

fter how many days would youe&pect it to have rained on '0

days?



nswer! 1(0 )days*



"wo fair tetrahedral )four-sided*dice are thrown% +f the faces of

each are numbered ', (, , and 9,what is the probability that the sumof the numbers on the bottom faces

is a prime?



nswer! 0



.hat is the shortest distance that canbe traveled if you start at any point, , /,

C, or and visit the other three pointsonce?

( ' /

2 (

C



nswer! 1'



How many positive integer pairs

)&, y* satisfy 3 & 4 y,'when 3 #?



nswer! ( )pairs*



+f the digit is placed to the rightof a three-digit number, forming

a four-digit number, the value ofthe original number increases by,000% .hat was the originalnumber?



nswer!



5ifty cards numbered 1 to (0 areplaced in a bo&% +f a card isselected at random, what is the

probability that the card is aprime number and a multiple of

seven? 6&press your answer asa common fraction%



1(0



.hat is the last digit in the

product of all natural numbersbetween 1 and 100?



nswer! 0



+f (7 is e&pressed as the product

of its prime factors in e&ponentialform, what is the sum of itse&ponents?



nswer! (



"his table shows the distribution of scores of 8r%Sampsons 10-point :ui;% .hat is the median score?

Test Scores Frequency10 I

9 II

8 III7 IIII

6 IIII

5

4 I

3

2 II



nswer!



certain type of < => by 11 paperhas a thic@ness of 0%0# cm% +f

1(,000 sheets of paper are stac@edon top of each other, what is the

height, in meters, of the stac@?



nswer! ' )meters*



Aoints , /, C, and are located on /such that / 3 ' 3 /C% +f a point is

selected at random, what is theprobability that it is between C and ?6&press your answer as a common

fraction%

C /



1#



"hree identical s:uares are

placed side by side to form arectangle with a perimeter of

102 inches% .hat is the area, ins:uare inches, of each s:uare?



nswer! 19 )s:uare inches*



/rad is less than '0 years old%

His age is a multiple of (% Be&tyear his age will be a multiple of% How old is /rad now?



nswer! #0 )years old*



How many different triangles are

in the figure?



nswer! 1' )triangles*



How many even numbers arebetween #01 and 20(?



nswer! 101



.hat is the positive s:uare rootof 1&1?



nswer! 2&<



.hen n is divided by (, the

remainder is 1% .hat is theremainder when 'n is divided by(?



nswer! '



6&press 10$ of '0$ of (0 as adecimal%



nswer! 1%(



3 1, #, ', 2, (, , , <, 9, DE%

.hat fractional part of the numbersin set are not divisible by '?



#'



Si& softball teams are to play

each other once% How manygames are needed?



nswer! 1( )games*



"wo ropes, 1< meters in lengthand #2 meters in length, need to

be cut into pieces which are allthe same length% .hat is thegreatest possible length of eachpiece?



nswer! )meters*



.hat value of n ma@es thissentence true?

n 3 n 4 1

9



nswer! #



+f f)&* 3 '& 4 # and g)&* 3 )& F 1*#

,what is f)g)-#**?



nswer! #9



+f 8arch 1 is a 8onday, what day ofthe wee@ will it be #0 days later?



nswer! 5riday



Given & 3 ' and y 3 #, simplify!

#&' F 'y#



nswer!



Simplify! 727'7



nswer! '(



+n how many different orders

can a group of si& people beseated around a round table?



nswer! 1#0 )ways*



How many different

arrangements are there usingthe letters in the wordAR6?



nswer! ''0 )arrangements*



.hat is I#00 to the nearest tenth?



nswer! 12%1



.hat is the positive geometricmean of < and 1<?



nswer! 1#



5ind the midpoint of the line

segment with endpoints )(, -(* and) -(, (*%



nswer! )0, 0*



Give the decimal e&pression for :$ of:%



nswer! 0%01:#



Solve for &! #& 4 # 3 1#<



nswer! (



"he area of a triangle is 00 s:uare

feet% 5ind the altitude, in feet, ofthe triangle if the length of the baseis '0 feet%



nswer! 20 )feet*



"he longest side of a right triangle

is ( feet and the shortest side is 'feet% .hat is the area of thetriangle in s:uare meters?



nswer! )s:uare meters*



+f each side of a s:uare is

increased by (0$, what is thepercent of increase in the area ofthe s:uare?



nswer! 1#( )percent*



5our lines are drawn in a plane%

.hat is the ma&imum number ofdistinct regions in which thelines could divide the plane?



nswer! 11



Simplify! 0%D 4 0%'''D0%999D



nswer! 1



.hat percent of <0$ of a

number will lave the numberunchanged?



nswer! 1#( )percent*



5ind the number of s:uare units inthe area of the shaded region%

)0, '0* )#0, '0* )'0, '0*

)'0, #0* )0, 10*



nswer! (00 )s:% units*



+f y 3 - 4 I)( F &*, find & when y 3'%



nswer! -9(



+n :uadrilateral /C, angle /and angle C are trisected asshown% .hat is the degree

measure of angle 5? / C

5



nswer! <0 )degrees*



5ind the number of s:uare units inthe area of the triangle%

)-#, *



nswer! '# )s:uare units*



.hat is the smallest integer thatsatisfies K#& F 'KL <?



nswer! -#



How many two-digit wholenumbers are divisible by 12?



nswer!



.hat percent of the whole

numbers less than 100 have noremainders when divided by (?



nswer! #0 )percent*



.hat is the 100

th

even wholenumber?



nswer! 19<

/C is a s:uare 2 inches on a side,



and each of the inside s:uares is

formed by Moining the midpoints of theouter s:uares sides% .hat is the areaof the shaded region?



nswer! 2 )s:uare inches*



+f all multiples of ' and allmultiples of 2 are removed from

the list of numbers 1 through100, how many whole numbers

are left?



nswer! (0 )whole numbers*



FINALS



ivide 2abc by #a#b 'd#



cd#

a



.hat is the simplest radicalform of 'I2 ÷ I#?



nswer! I#



"wo fair cubical dice are tossed%.hat is the probability,

e&pressed as a commonfraction, that the sum of thenumbers showing on the dice

will be four?



11#



+f a N b is defined as a 4 b,

#what is the value of N )' N (*?



nswer! (



+f & and y are positive integers

such that &y 3 10<, what is theleast possible value of & 4 y?



nswer! #1



5ind II#(,000%



nswer! 20



6&press the value of1 of 10$ of 0%001 in scientific notation%

100



nswer! 1 or)1%0* J 10-



5ind the sum of all solutions to

this e:uation!&# 4 # 3 10#



nswer! 0



.hat is the sum of the lengths, incentimeters, of the two legs of a

'0-0-90 right triangle, if the lengthof the hypotenuse is #I cm?



nswer! I 4 'I#



How many diagonals can bedrawn for a he&agon?



nswer! 9 )diagonals*

1991 State Countdown Round

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