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GRADUATE RECORD EXAMINATIONS®

Practice General Test #2Section 3: Quantitative ReasoningSection 4: Quantitative Reasoning

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Instructions for the Verbal Reasoning and Quantitative Reasoning SectionsInformation for screen reader users:This document has been created to be accessible to individuals who use screen readers. You may wish to consult the manual or help system for your screen reader to learn how best to take advantage of the features implemented in this document. Please consult the separate document, GRE Screen Reader Instructions.doc, for important details.

This practice test includes content that some users may wish to skip. For example, some questions require you to complete sentences or longer texts from among several choices. For those questions where it might be helpful to hear the available choices in context, text of the choices in context is included. However, some users may wish to skip this material. Similarly, some questions include detailed figure descriptions that some users may wish to skip because they can get the required information from the accompanying tactile or large print figures. In each case, material that may be skipped is delineated by statements like “Begin skippable content” and “End skippable content” each in the Heading 6 style.

As a reminder, standard timing for each section of the test is provided in the table below:

Section Order Section Name Standard Time

Analytical Writing 1 Analyze an Issue 30 minutes

Analytical Writing 2 Analyze an Argument 30 minutes

1 Verbal Reasoning 35 minutes

2 Verbal Reasoning 35 minutes

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3 Quantitative Reasoning 40 minutes

4 Quantitative Reasoning 40 minutes

The Quantitative sections include figures and their descriptions. In addition, separate figure supplements, in large print (18 points) and raised line formats, are available. The large print figure supplement may be downloaded from www.gre.org. To obtain the raised line figure supplement or if you have difficulty locating the large print figure supplement on the GRE® web site, contact E T S Disability Services Monday to Friday 8:30 a.m. to 4:30 p.m. New York time, 1-609-771-7780, 1-866-387-8602 (toll free for test takers in the United States, U.S. Territories, and Canada). E-mail: [email protected].

Important NotesIn the actual test, your scores for the multiple choice sections will be determined by the number of questions you answer correctly. Nothing is subtracted from a score if you answer a question incorrectly. Therefore, to maximize your scores it is better for you to guess at an answer than not to respond at all. Work as rapidly as you can without losing accuracy. Do not spend too much time on questions that are too difficult for you. Go on to the other questions and come back to the difficult ones later.

Some or all of the passages in this test have been adapted from published material to provide the examinee with significant problems for analysis and evaluation. To make the passages suitable for testing purposes, the style, content, or point of view of the original may have been altered. The ideas contained in the passages do not necessarily represent the opinions of the Graduate Record Examinations Board or Educational Testing Service.

You may use a calculator in the Quantitative Reasoning sections only. You will be provided with a basic calculator and cannot use any other calculator, except as an approved accommodation.

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mailto:[email protected]

http://www.gre.org/

Marking Your AnswersIn the actual test, all answers must be entered in the test book (or in the supervisor’s copy of the test book if you are not using a print format test). If answers are being recorded in a large print test book, the directions for marking answers are slightly different because answers entered in large print test books are not machine-scored.

If your answers are being entered in a large print test book, make sure your marks are clear and unambiguous. Additional instructions for marking answers in large print test books are provided with the large print practice tests.

The following instructions describe how answers must be filled in if using a regular print test book, whether you are entering your own answers or a scribe is entering them at your direction.

Be sure that each mark is dark and completely fills the circle.

Any stray marks that lie in or near a circle must be erased carefully. If you change an answer, be sure that all previous marks are erased completely. Stray marks and incomplete erasures may be read as intended answers. You may work out your answers in the blank areas of the test book, but do not work out answers near the circles. Scratch paper will not be provided, except as an approved accommodation.

Question FormatsThis practice test may include questions that would not be used in an actual test administered in an alternate format because they have been determined to be less suitable for presentation in such formats.

The questions in these sections have several different formats. A brief description of these formats and instructions for entering your answer choices are given below.

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Multiple-Choice Questions—Select One Answer ChoiceThese standard multiple-choice questions require you to select just one answer choice from a list of options. You will receive credit only if you mark the single correct answer choice and no other.

Example:

What city is the capital of France?

A. Rome

B. Paris

C. London

D. Cairo

In this example, B, Paris, should be marked.

Multiple-Choice Questions—Select One or More Answer ChoicesSome of these questions specify how many answer choices you must select; others require you to select all that apply. In either case, to receive credit all of the correct answer choices must be marked. In printed versions of the test, these questions are distinguished by the use of a square box to select an answer choice.

Example:

Select all that apply.

Which of the following countries are in Africa?

A. Chinadocument.doc of 58

B. Congo

C. France

D. Kenya

In this example, B and D (Congo and Kenya) should be marked.

Column Format QuestionsThis question type presents the answer choices in groups (presented as columns in the printed version of the test). You must pick one answer choice from each group. You will receive credit only if you mark the correct answer choice in each group. In the following example, there is a sentence with two blanks, each indicating that something has been omitted. For each question of this type, first you will hear the text with the word “BLANK” in place of the omitted material. Next, you will hear the text again, but in place of each blank, you will hear three lettered options for filling that blank. The set of lettered options is formatted as bold and enclosed in parentheses. Each option consists of a word or phrase.

For questions containing one or two blanks, following the list of answer choices are up to nine readings of the text, one for each answer choice combination. The group of readings begins with a “Begin Skippable Content” level-6 heading and ends with an “End Skippable Content” level-6 heading. Each reading consists of the option letter or letters, the words or phrases being combined, and the text with the combination of the words or phrases inserted into the blanks.

For questions containing three blanks, the choices will not be read in context because it has been determined that replaying the question for all possible combinations of answer choices is not a useful way to present these questions.

Example:

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This question has two blanks.

Complete the following sentence.

BLANK is the capital of BLANK.

Now listen to the text with the three options inserted in place of each blank.

(A. Paris, B. Rome, C. Cairo) is the capital of (D. Canada, E. France, F. China).

Indicate your two answer choices and skip hearing the answer choices in context or go on to hear them in context before indicating your answer choices. Fill all blanks in the way that best completes the text.

Begin skippable content.Answer Choices in Context:

A, D. Paris, Canada. Paris is the capital of Canada.

A, E. Paris, France. Paris is the capital of France.

A, F. Paris, China. Paris is the capital of China.

B, D. Rome, Canada. Rome is the capital of Canada.

B, E. Rome, France. Rome is the capital of France.

B, F. Rome, China. Rome is the capital of China.

C, D. Cairo, Canada. Cairo is the capital of Canada.

C, E. Cairo, France. Cairo is the capital of France.

C, F. Cairo, China. Cairo is the capital of China.

End skippable content.

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Indicate your two answer choices. Fill all blanks in the way that best completes the text.

In this example, choice A, Paris (from the group A, B, C), and E, France (from the group D, E, F), should be indicated as the answer.

Numeric Entry QuestionsThese questions require a number to be entered by marking entries in a grid according to the following instructions.

1. Your answer may be an integer, a decimal, or a fraction, and it may be negative.2. Equivalent forms of the correct answer, such as 2.5 and 2.50, are all correct. Although

fractions do not need to be reduced to lowest terms, they may need to be reduced to fit in the grid.

3. Enter the exact answer unless the question asks you to round your answer.4. If a question asks for a fraction, the grid will have a built-in division slash. Otherwise,

the grid will have a decimal point.

The instructions for marking the entries will depend on whether a regular print or a large print test is being used to record your answers. If your answers are being entered into a regular print edition of the test, the following instructions apply:

5. Start your answer in any column, space permitting. Fill in no more than one entry in any column of the grid. Columns not needed should be left blank.

6. Write your answer in the boxes at the top of the grid and fill in the corresponding circles. You will receive credit only if your grid entries are clearly marked, regardless of the number written in the boxes at the top.

If your answers are being entered into a large print edition of the test, instead of filling in circles on the grid in steps 5 and 6, you will be asked to circle those entries.

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Section 3 follows. In an actual test, testing time will resume when you begin the section 3.

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Section 3. Quantitative Reasoning

25 Questions

Directions:For each question, indicate the best answer, using the directions given.

Notes: All numbers used are real numbers.

All figures are assumed to lie in a plane unless otherwise indicated.

Geometric figures, such as lines, circles, triangles, and quadrilaterals, are not necessarily drawn to scale. That is, you should not assume that quantities such as lengths and angle measures are as they appear in a figure. You should assume, however, that lines shown as straight are actually straight, points on a line are in the order shown, and more generally, all geometric objects are in the relative positions shown. For questions with geometric figures, you should base your answers on geometric reasoning, not on estimating or comparing quantities from how they are drawn in the geometric figure.

Coordinate systems, such as x y planes and number lines, are drawn to scale; therefore, you can read, estimate, or compare quantities in such figures from how they are drawn in the coordinate system.

Graphical data presentations, such as bar graphs, circle graphs, and line graphs, are drawn to scale; therefore, you can read, estimate, or compare data values from how they are drawn in the graphical data presentation.

For each of Questions 1 through 9, compare Quantity A and Quantity B, using the additional information given, if any. Select one of the following four answer choices.

A. Quantity A is greater.

B Quantity B is greater.

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C. The two quantities are equal.

D. The relationship cannot be determined from the information given.

A symbol that appears more than once in a question has the same meaning throughout the question.

Example 1:

Quantity A: 2 times 6

Quantity B: 2 + 6

Solution: Quantity A is equal to 12 and Quantity B is equal to 8, so the correct answer for Example 1 is answer choice A, Quantity A is greater.

Example 2:

Refer to the figure.

Figure for Example 2

Begin skippable part of figure description.The figure for example 2 shows triangle PQR, where P is the leftmost vertex of the horizontal base PR and vertex Q is above PR. Point S lies on horizontal base PR and appears to be the midpoint of PR. Line segment QS is drawn from vertex Q to point S. The lengths of PS and SR appear to be equal.

End skippable part of figure description.document.doc of 58

Quantity A: The length of PS

Quantity B: The length of SR

Solution: The correct answer for Example 2 is answer choice D. The relationship between the lengths of PS and SR cannot be determined from the information given since equal measures cannot be assumed, even though the lengths of PS and SR appear to be equal in the figure.

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Question 1.Refer to the figure.

Figure for Question 1

The figure shows a circle with center O, and four line segments.

Begin skippable part of figure description.The first line segment starts at the center of the circle and ends at a point inside the circle. The second line segment, which is perpendicular to the first, starts at the point inside the circle where the first segment ended and ends at a point on the circle. The first and the second line segments are of lengths x and 3, respectively. The third line segment starts at the center of the circle and ends at a point inside the circle. The fourth line segment, which is perpendicular to the third, starts at the point inside the circle where the third segment ended and ends at a point on the circle. The third and fourth line segments are of lengths 3 and 4, respectively.

End skippable part of figure description.It is given that O is the center of the circle in the figure for question 1 above.

Quantity A: x

Quantity B: 5document.doc of 58


B. Quantity B is greater.


D. The relationship cannot be determined from the information given

From the answer choices given, select and indicate the one that describes the relationship between quantity A and quantity B.

Question 2.

Runner A ran four fifths kilometer and Runner B ran 800 meters.

Quantity A: The distance that A ran

Quantity B: The distance that B ran






Question 3.It is given that x is less than y, which is less than z.

Quantity A: the fraction with numerator x + y + z, and denominator 3

Quantity B: y

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The figure shows a right triangle with a vertical leg and a horizontal leg.

Begin skippable part of figure description.The angle formed by the vertical leg and the horizontal leg measures 90°. The length of the vertical leg is x, and the length of the horizontal leg is y. The angle opposite the vertical leg measures 50°.


Quantity A: x over y

Quantity B: 1






Question 5.

It is given that 0 is less than x, which is less than y, which is less than 1.

Quantity A: 1 minus y

Quantity B: y minus x






Question 6.

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It is given that p is the probability that event E will occur, and s is the probability that event E will not occur.

Quantity A: p + s

Quantity B: ps






Question 7.

It is given that X is the set of all integers n that satisfy the inequality 2 is less than or equal to the absolute value of n, which is less than or equal to 5.

Quantity A: The absolute value of the greatest integer in X

Quantity B: The absolute value of the least integer in X






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Question 8.It is given that x and m are positive numbers, and m is a multiple of 3.

Quantity A: the fraction with numerator x raised to the m power, and denominator x raised to the third power

Quantity B: x, raised to the m over 3 power






Question 9.A random variable Y is normally distributed with a mean of 200 and a standard deviation of 10.

Quantity A: The probability of the event that the value of Y is greater than 220

Quantity B: 1 sixth




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Questions 10 through 25 have several different answer formats, including both selecting answers from a list of answer choices and numeric entry. With each question, answer format instructions will be given.

Numeric Entry QuestionsThese questions require a number to be entered by marking entries in a grid according to the following instructions.

1. Your answer may be an integer, a decimal, or a fraction, and it may be negative.

2. Equivalent forms of the correct answer, such as 2.5 and 2.50, are all correct. Although fractions do not need to be reduced to lowest terms, they may need to be reduced to fit in the grid.

3. Enter the exact answer unless the question asks you to round your answer.

4. If a question asks for a fraction, the grid will have a built in division slash. Otherwise, the grid will have a decimal point.



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Question 10.This question has five answer choices, labeled A through E. Select the best one of the answer choices given.

The ratio of 1 third to 3 eighths is equal to the ratio of

A. 1 to 8

B. 8 to 1

C. 8 to 3

D. 8 to 9

E. 9 to 8

Select and indicate the best one of the answer choices given.


A reading list for a humanities course consists of 10 books, of which 4 are biographies and the rest are novels. Each student is required to read a selection of 4 books from the list, including 2 or more biographies. How many selections of 4 books satisfy the requirements?

A. 90

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B. 115

C. 130

D. 144

E. 195


Question 12.This question does not have any answer choices; it is a numeric entry question. To answer this question, enter a number in the answer space provided.

In a graduating class of 236 students, 142 took algebra and 121 took chemistry. What is the greatest possible number of students that could have taken both algebra and chemistry?

The answer space is followed by the word “students”.

To answer this question, enter a number in the answer space provided. The number can include a decimal point, and can be positive, negative, or zero. The number entered cannot be a fraction.



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The figure shows three lines. Two horizontal parallel lines m and k, where line m is above line k, and a third line that intersects both line k and line m.

Begin skippable part of figure description.The third line extends from the lower left of the figure to the upper right of the figure. The angle above line m and to the left of the third line measures sº. The angle above line k and to the right of the third line measures tº.

End skippable part of figure description.In the figure for question 13 above, if line m is parallel to line k and s = t + 30, then t =

A. 30

B. 60

C. 75

D. 80

E. 105


Question 14.

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This question has five answer choices, labeled A through E. Select the best one of the answer choices given.

If 2x = 3y = 4z = 20, then 12 x y z =

A. 16,000

B. 8,000

C. 4,000

D. 800

E. 10


Question 15.This question has three answer choices, labeled A through C. Select all the answer choices that apply.

The total amount that Mary paid for a book was equal to the price of the book plus a sales tax that was 4 percent of the price of the book. Mary paid for the book with a $10 bill and received the correct change, which was less than $3.00. Which of the following statements must be true?

Indicate all such statements.

A. The price of the book was less than $9.50.

B. The price of the book was greater than $6.90.

C. The sales tax was less than $0.45.

Select and indicate all the answer choices that apply. The correct answer to a question of this type could consist of as few as one, or as many as all three of the answer choices.

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If the fraction with numerator 1, and denominator 2 raised to the eleventh power, times 5 raised to the seventeenth power is expressed as a terminating decimal, how many nonzero digits will the decimal have?

A. One

B. Two

C. Four

D. Six

E. Eleven


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Questions 17 through 20 are based on the following data.

Data for Questions 17 through 20

The data shown is a bar graph. The title of the bar graph is “Variation in the Amount of Caffeine in Common Beverages and Drugs”.

Begin skippable part of data description.Accompanying the graph is a note stating that the data are based on 5 ounce cups of coffee, tea, and cocoa, 12 ounce cups of soft drinks, and single doses of drugs, and a note stating that the source of the data is the Food and Drug Administration.

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In the graph there are eleven types of beverages and drugs that are grouped into 3 categories: Coffee, Other beverages, and Drugs. The three categories, along with the 11 types of beverages and drugs in them, are listed on the left side of the graph. For each beverage or drug listed, there is a horizontal bar associated with it that extends from the minimum to the maximum amount of caffeine in that beverage or drug. The horizontal axis of the graph is labeled Amount of Caffeine, in milligrams, and there are vertical gridlines from 0 to 200, in increments of 25.

The bars in the graph are as follows. (Note: data values are approximate.)

For beverages in the Coffee category:

Decaffeinated coffee: The bar extends from 0 to 10 milligrams.

Percolated coffee: The bar extends from 35 to 170 milligrams

Drip brewed coffee: The bar extends from 60 to 180 milligrams

Instant coffee: The bar extends from 30 to 120 milligrams.

For beverages in the Other beverages category:

Brewed tea: The bar extends from 20 to 110 milligrams.

Instant tea: The bar extends from 25 to 50 milligrams.

Cocoa: The bar extends from 5 to 20 milligrams.

Caffeinated soft drinks: The bar extends from 30 to 60 milligrams.

For types of Drugs.

Weight loss drugs, diuretics, and stimulants: The bar extends from 100 to 200 milligrams.

Pain relievers: The bar extends from 35 to 100 milligrams.

Cold allergy remedies: The bar extends from 20 to 35 milligrams.

End skippable part of data description.

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The least amount of caffeine in a 5 ounce cup of drip brewed coffee exceeds the greatest amount of caffeine in a 5 ounce cup of cocoa by approximately how many milligrams?

A. 160

B. 80

C. 60

D. 40

E. 20


Question 18.This question does not have any answer choices; it is a numeric entry question.

To answer this question, enter a number in the answer space provided.

For how many of the 11 categories of beverages and drugs listed in the graph can the amount of caffeine in the given serving size be less than 50 milligrams?

The answer space is followed by the word “categories”.


Question 19.document.doc of 58


Approximately what is the minimum amount of caffeine, in milligrams, consumed per day by a person who daily drinks two 10 ounce mugs of percolated coffee and one 12 ounce cup of a caffeinated soft drink?

A. 230

B. 190

C. 140

D. 110

E. 70



Which of the following shows the four types of coffee listed in order according to the range of the amounts of caffeine in a 5 ounce cup, from the least range to the greatest range?

A. Decaffeinated, instant, percolated, drip brewed

B. Decaffeinated, instant, drip brewed, percolated

C. Instant, decaffeinated, drip brewed, percolated

D. Instant, drip brewed, decaffeinated, percolated

E. Instant, percolated, drip brewed, decaffeinated


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Begin skippable part of figure description.The title of the graph for question 21 is “Energy Used per Meter Versus Speed During Running and Walking”.

In the graph, the horizontal axis is labeled Speed (miles per hour). There are labeled vertical gridlines at 1, 2, 3, 4, and 5, and unlabeled vertical gridlines at 0.5, 1.5, 2.5, 3.5, and 4.5. The vertical axis is labeled Energy Used per Meter (joules per meter). There are labeled horizontal gridlines at 100, 200, and 300. There are unlabeled horizontal gridlines at 50, 150, 250, and 350.

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The graph shows a solid Running curve and a dashed Walking curve. Both curves show the energy used per meter, in joules per meter, for speeds between 2 miles per hour and 5 miles per hour. The Running curve goes down for speeds from 2 to 4 miles per hour and goes up for speeds from 4 to 5 miles per hour. The running curve is above the walking curve between 2 miles per hour and 4.7 miles per hour where the two curves intersect. The walking curve goes up for all speeds from 2 miles per hour to 5 miles per hour and intersects with the running curve at speed 4.7 miles per hour. The walking curve is above the running curve between 4.7 and 5 miles per hour.

End skippable part of figure description.If s is a speed, in miles per hour, at which the energy used per meter during running is twice the energy used per meter during walking, then, according to the figure for question 21 above, s is between

A. 2.5 and 3.0

B. 3.0 and 3.5

C. 3.5 and 4.0

D. 4.0 and 4.5

E. 4.5 and 5.0



If n = 2 cubed, then n raised to the power n =

A. 2 raised to the power 6

B. 2 raised to the power 11

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C. 2 raised to the power 18

D. 2 raised to the power 24

E. 2 raised to the power 27


Question 23.This question has five answer choices, labeled A through E. Select all the answer choices that apply.



The figure shows a right triangle ABC.

Begin skippable part of figure description.In the right triangle ABC, hypotenuse AC is horizontal, with point C to the right of point A; vertex B is above the hypotenuse AC, and the angle ABC measures 90º. Point D lies on the hypotenuse AC and divides triangle ABC into two smaller triangles ABD and BCD.

End skippable part of figure description.

It is given that the length of AB is 10 times the positive square root of 3.

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Which of the following statements individually provide(s) sufficient additional information to determine the area of triangle ABC in the figure for question 23 above?


A. DBC is an equilateral triangle.

B. ABD is an isosceles triangle.

C. The length of BC is equal to the length of AD.

D. The length of BC is 10.

E. The length of AD is 10.

Select and indicate all the answer choices that apply. The correct answer to a question of this type could consist of as few as one, or as many as all five of the answer choices.

Question 24.This question does not have any answer choices; it is a numeric entry question. To answer this question, enter a number in the answer space provided.

In the sequence a sub 1, a sub 2, a sub 3, dot dot dot, a sub n, dot dot dot, each term after the first term is equal to the preceding term plus the constant c. If

a sub 1, +, a sub 3, +, a sub 5, =, 27, what is the value of a sub 2, +, a sub 4 ?

The answer space is preceded by “a sub 2, +, a sub 4, =”


Question 25.document.doc of 58


A desert outpost has a water supply that is sufficient to last 21 days for 15 people. At the same average rate of water consumption per person, how many days would the water supply last for 9 people?

A 28.0

B. 32.5

C. 35.0

D. 37.5

E. 42.0


This is the end of Section 3 of Revised GRE Practice Test Number 2. In an actual test, once you complete a section you may not return to it. The answer key for this section is in a separate document, titled "GRE Practice Test 2 Answers.doc". Explanations for the questions in this section are in a separate document, titled “GRE Practice Test 2 Quant Explanations.doc.”

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SECTION 4. Quantitative Reasoning

25 Questions

Directions:For each question, indicate the best answer, using the directions given.

Notes: All numbers used are real numbers.

All figures are assumed to lie in a plane unless otherwise indicated.

Geometric figures, such as lines, circles, triangles, and quadrilaterals, are not necessarily drawn to scale. That is, you should not assume that quantities such as lengths and angle measures are as they appear in a figure. You should assume, however, that lines shown as straight are actually straight, points on a line are in the order shown, and more generally, all geometric objects are in the relative positions shown. For questions with geometric figures, you should base your answers on geometric reasoning, not on estimating or comparing quantities from how they are drawn in the geometric figure.

Coordinate systems, such as x y planes and number lines, are drawn to scale; therefore, you can read, estimate, or compare quantities in such figures from how they are drawn in the coordinate system.

Graphical data presentations, such as bar graphs, circle graphs, and line graphs, are drawn to scale; therefore, you can read, estimate, or compare data values from how they are drawn in the graphical data presentation.

For each of Questions 1 through 9, compare Quantity A and Quantity B, using the additional information given, if any. Select one of the following four answer choices.


B Quantity B is greater.

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A symbol that appears more than once in a question has the same meaning throughout the question.

Example 1:

Quantity A: 2 times 6

Quantity B: 2 + 6

Solution: Quantity A is equal to 12 and Quantity B is equal to 8, so the correct answer for Example 1 is answer choice A, Quantity A is greater.

Example 2:


Figure for Example 2

Begin skippable part of figure description.The figure for example 2 shows triangle PQR, where P is the leftmost vertex of the horizontal base PR and vertex Q is above PR. Point S lies on horizontal base PR and appears to be the midpoint of PR. Line segment QS is drawn from vertex Q to point S. The lengths of PS and SR appear to be equal.


Quantity A: The length of PS

Quantity B: The length of SR

Solution: The correct answer for Example 2 is answer choice D. The relationship between the lengths of PS and SR cannot be determined from the information given since equal measures cannot be assumed, even though the lengths PS and SR appear to be equal in the figure.

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Question 1.The value of 1 United States dollar is 0.93 Argentine peso and the value of 1 United States dollar is 32.08 Kenyan shillings.

Quantity A: The dollar value of 1 Argentine peso

Quantity B: The dollar value of 1 Kenyan shilling






Question 2.It is given that k is a digit in the decimal 1.3k5, and 1.3k5 is less than 1.33.

Quantity A: k

Quantity B: 1






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The figure is a circle. Points A, B, C, and D lie on the circle.

Begin skippable part of figure description.Point A is the lowermost, and point B the uppermost, point on the circle. Point C lies on the circle a little to the left of point B, and point D lies on the circle, a little to the right of point B. Diameter AB, and the two chords AC and AD have been drawn. Diameter AB appears to be slightly longer than chord AC and slightly longer than chord AD.

End skippable part of figure description.It is given that AB is a diameter of the circle in the figure for question 3.

Quantity A: The length of AB

Quantity B: The average (arithmetic mean) of the lengths of AC and AD





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Question 4.

It is given that st, =, the positive square root of 10.

Quantity A: s squared

Quantity B: the fraction with numerator 10, and denominator t squared






Question 5.It is given that three consecutive integers have a sum of negative 84.

Quantity A: The least of the three integers

Quantity B: negative 28




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Question 6.

In the x y plane, the equation of line k is 3x minus 2y, = 0.

Quantity A: The x intercept of line k

Quantity B: The y intercept of line k

A Quantity A is greater.





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Question 7.It is given that n is a positive integer that is divisible by 6.

Quantity A: The remainder when n is divided by 12

Quantity B: The remainder when n is divided by 18






Question 8.

It is given that the fraction with numerator 1 minus x, and denominator x minus 1, = the fraction 1 over x

Quantity A: x

Quantity B: negative one half





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Question 9.In a set of 24 positive integers, 12 of the integers are less than 50. The rest are greater than 50.

Quantity A: The median of the 24 integers

Quantity B: 50






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Questions 10 through 25 have several different answer formats, including both selecting answers from a list of answer choices and numeric entry. With each question, answer format instructions will be given.

Numeric Entry Questions

These questions require a number to be entered by marking entries in a grid according to the following instructions.

1. Your answer may be an integer, a decimal, or a fraction, and it may be negative.

2. Equivalent forms of the correct answer, such as 2.5 and 2.50, are all correct. Although fractions do not need to be reduced to lowest terms, they may need to be reduced to fit in the grid.

3. Enter the exact answer unless the question asks you to round your answer.

4. If a question asks for a fraction, the grid will have a built in division slash. Otherwise, the grid will have a decimal point.





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The fabric needed to make 3 curtains sells for $8.00 per yard and can be purchased only by the full yard. If the length of fabric required for each curtain is 1.6 yards and all of the fabric is purchased as a single length, what is the total cost of the fabric that needs to be purchased for the 3 curtains?

A. $40.00

B. $38.40

C. $24.00

D. $16.00

E. $12.80



In the x y plane, line k is a line that does not pass through the origin.

Which of the following statements individually provide(s) sufficient additional information to determine whether the slope of line k is negative?


A. The x intercept of line k is twice the y intercept of line k.

B. The product of the x intercept and the y intercept of line k is positive.

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C. Line k passes through the points a comma b, and r comma s, where

open parenthesis, a minus r, close parenthesis, times, open parenthesis, b minus s, close parenthesis, is less than 0.



The distance from Centerville to a freight train is given by the expression negative 10t, +, 115, and the distance from Centerville to a passenger train is given by the

expression negative 20t, +, 150.

The expressions above give the distance from Centerville to each of two trains t hours after 12:00 noon. At what time after 12:00 noon will the trains be equidistant from Centerville?

A. 1:30

B. 3:30

C. 5:10

D. 8:50

E. 11:30



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The company at which Mark is employed has 80 employees, each of whom has a different salary. Mark’s salary of $43,700 is the second highest salary in the first quartile of the 80 salaries. If the company were to hire 8 new employees at salaries that are less than the lowest of the 80 salaries, what would Mark’s salary be with respect to the quartiles of the 88 salaries at the company, assuming no other changes in the salaries?

A. The fourth highest salary in the first quartile

B. The highest salary in the first quartile

C. The second lowest salary in the second quartile

D. The third lowest salary in the second quartile

E. The fifth lowest salary in the second quartile



To answer this question, enter a number in the answer space provided.

In the x y plane, the point with coordinates negative 6 comma negative 7 is the

center of circle C. The point with coordinates negative 6 comma 5 lies inside C, and

the point with coordinates 8 comma negative 7 lies outside C. If m is the radius of C and m is an integer, what is the value of m ?

The answer space is preceded by “m =”.


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If negative m over 19 is an even integer, which of the following must be true?

A. m is a negative number.

B. m is a positive number.

C. m is a prime number.

D. m is an odd integer.

E. m is an even integer.



The integer v is greater than 1. If v is the square of an integer, which of the following numbers must also be the square of an integer?

Indicate all such numbers.

A. 81v

B. 25v, +, 10 times the positive square root of v, +, 1

C. 4, v squared, +, 4 times the positive square root of v, +, 1


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Questions 17 through 20 are based on the following data, which consists of two graphs.

Data for Questions 17 through 20 – Graph 1

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Data for Questions 17 through 20 – Graph 2

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Begin skippable part of data description.The title of the data is “Distance Traveled by a Car According to the Car’s Speed when the Driver is Signaled to Stop”.

The data consists of two graphs.

The title of the first graph is “Distance Traveled During Reaction Time”. The title of the second graph is “Distance Traveled After Brakes Have Been Applied”. There are two notes accompanying the graphs. The first note defines reaction time as follows: “Reaction time is the time period that begins when the driver is signaled to stop and ends when the driver applies the brakes”. The second note says “Total stopping distance is the sum of the distance traveled during reaction time and the distance traveled after brakes have been applied”.

In both graphs, the horizontal axis is labeled “Speed (miles per hour)”, and the vertical axis is labeled “Distance (feet)”.

In the first graph, “Distance Traveled During Reaction Time”, along the horizontal axis, speeds from 0 to 80 miles per hour, in increments of 10, are labeled; and, in addition, there are vertical gridlines at speeds from 0 to 80 miles per hour, in increments of 5. Along the vertical axis, distances from 0 to 90 feet, in increments of 10, are labeled; and, in addition, there are horizontal gridlines at distances from 0 to 90 feet, in increments of 5.

The first graph is a line from the point with coordinates 0 comma 0, to the point with coordinates 80 comma 88.

For each point on the line, the first coordinate represents speed in miles per hour and the second coordinate represents Distance in feet. The following are the coordinates of nine points on the line:

40 comma 44

45 comma 49.5

50 comma 55

55 comma 60.5

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60 comma 66

65 comma 71.5

70 comma 77

75 comma 82.5

80 comma 88

In the second graph “Distance Traveled After Brakes Have Been Applied”, along the horizontal axis, speeds from 0 to 80 miles per hour, in increments of 10, are labeled; and, in addition, there are vertical gridlines at speeds from 0 to 80 miles per hour, in increments of 5. Along the vertical axis, distances from 0 to 400 feet, in increments of 50 are labeled; and, in addition, there are horizontal gridlines at distances from 0 to 400, in increments of 25.

The second graph is a curve that begins at 0 comma 0, and increases, at first gradually, then more quickly.

For each point on the curve, the first coordinate represents speed in miles per hour and the second coordinate represents Distance in feet. Four points marked on the curve have the following coordinates:

40 comma 88

50 comma 137

60 comma 198

70 comma 269

End skippable part of data description.


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The speed, in miles per hour, at which the car travels a distance of 52 feet during reaction time is closest to which of the following?

A. 43

B. 47

C. 51

D. 55

E. 59



Approximately what is the total stopping distance, in feet, if the car is traveling at a speed of 40 miles per hour when the driver is signaled to stop?

A. 130

B. 110

C. 90

D. 70

E. 40


Question 19.

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Of the following, which is the greatest speed, in miles per hour, at which the car can travel and stop with a total stopping distance of less than 200 feet?

A. 50

B. 55

C. 60

D. 65

E. 70



The total stopping distance for the car traveling at 60 miles per hour is approximately what percent greater than the total stopping distance for the car traveling at 50 miles per hour?

A. 22%

B. 30%

C. 38%

D. 45%

E. 52%


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What is the least positive integer that is not a factor of 25 factorial and is not a prime number?

A. 26

B. 28

C. 36

D. 56

E. 58



If 0 is less than a, which is less than 1, which is less than b, which of the following is true about the reciprocals of a and b ?

A. 1 is less than 1 over a, which is less than 1 over b

B. 1 over a is less than 1, which is less than 1 over b

C. 1 over a is less than 1 over b, which is less than 1

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E. 1 over b is less than 1 over a, which is less than 1





The figure consists of two circles and a shaded quadrilateral.

Begin skippable part of figure description.Each circle passes through the center of the other and the circles intersect at two points. The center of one circle is labeled O, and the center of the other circle is labeled P. The vertices of the shaded quadrilateral are O, one of the points of intersection of the two circles, P, and the other point of intersection of the two circles.

End skippable part of figure description.In the figure for question 23 above, O and P are the centers of the two circles. If each circle has radius r, what is the area of the shaded region?

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A. the positive square root of 2, over 2, times r squared

B. the positive square root of 3, over 2, times r squared

C. the positive square root of 2, times r squared

D. the positive square root of 3, times r squared

E. 2 times, the positive square root of 3, times r squared



To answer this question, enter a fraction in the answer space provided.

Of the 20 lightbulbs in a box, 2 are defective. An inspector will select 2 lightbulbs simultaneously and at random from the box. What is the probability that neither of the lightbulbs selected will be defective?

Give your answer as a fraction.

To answer this question, enter a fraction in the answer space provided. The fraction can be positive or negative. Neither the numerator nor the denominator of the fraction can include a decimal point. The fraction does not have to be in lowest terms.


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What is the perimeter, in meters, of a rectangular playground 24 meters wide that has the same area as a rectangular playground 64 meters long and 48 meters wide?

A. 112

B. 152

C. 224

D. 256

E. 304


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This is the end of Section 4 of Revised GRE Practice Test Number 2. In an actual test, once you complete a section you may not return to it. The answer key for this section is in a separate document, titled "GRE Practice Test 2 Answers.doc". Explanations for the questions in this section are in a separate document, titled “GRE Practice Test 2 Quant Explanations.doc.”

This is the end of Section 4 of Revised GRE Practice Test Number 2. In an actual test, once you complete a section you may not return to it. The answer key for this section is in a separate document, titled "GRE Practice Test 2 Answers.doc". Explanations for the questions in this section are in a separate document, titled “GRE Practice Test 2 Quant Explanations.doc”

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GRE Practice Test 2 Quant - ETS Home · Web viewAlong the vertical axis, distances from 0 to 400...

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