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GRE® General Test: Quantitative Reasoning Sample Questions

The GRE® Quantitative Reasoning section contains four types of questions:

  • Quantitative Comparison Questions
  • Multiple-choice Questions — Select One Answer Choice
  • Multiple-choice Questions — Select One or More Answer Choices
  • Numeric Entry Questions

Each question appears either independently as a discrete question or as part of a set of questions called a Data Interpretation set. All of the questions in a Data Interpretation set are based on the same data presented in tables, graphs or other displays of data. Below are descriptions, directions and samples of each type of question.

Quantitative Comparison Questions

Questions of this type ask the test taker to compare two quantities — Quantity A and Quantity B — and then determine which of four statements describes the comparison.

Sample Questions

Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices.

  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal.
  4. 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.

1.

Quantity A
x squared + 1
Quantity B
2x, minus 1
  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal.
  4. The relationship cannot be determined from the information given.

Correct Answer: A

The figure for sample question 2 shows parallelogram RSTU. Sides R U and S T are horizontal, with S T above, and slightly to the left of side R U. Diagonal S U, which extends from vertex S at the upper left of the parallelogram to vertex U at the lower right of the parallelogram, divides the parallelogram into two triangles, R S U and U S T; and the angle at vertex S into 2 adjacent angles R S U and U S T. The measure of angle R S U is x degrees, and the measure of angle U S T is y degrees. End of figure description.

RSTU is a parallelogram.

2.

Quantity A
x
Quantity B
y
  1. Quantity A is greater.
  2. Quantity B is greater.
  3. The two quantities are equal.
  4. The relationship cannot be determined from the information given.

Correct Answer: D

Multiple-choice Questions — Select One Answer Choice

These questions are multiple-choice questions that ask the test taker to select only one answer choice from a list of five choices.

Sample Questions

Select a single answer choice.

The figure for sample question 1 is a circle with center C. Two diameters of the circle are drawn, dividing the circle into 4 sectors, Two nonadjacent sectors are shaded, and the central angle of one of the unshaded sections measures 160 degrees. End of figure description.

1. The figure above shows a circle with center C and radius 6. What is the sum of the areas of the two shaded regions?

  1. 7.5 pi
  2. 6 pi
  3. 4.5 pi
  4. 4 pi
  5. 3 pi

Correct Answer: D

The figure for sample question 2 shows the graph in the x y plane of the function f of x = the absolute value of 2x, end absolute value, + 4. There are equally spaced tick marks along the x axis and along the y axis. The first tick mark to the right of the origin, and the first tick mark above the origin, are both labeled 1. The graph of the function f is in the shape of the letter V. It is above the x axis and is symmetric with respect to the y axis. The lowest point on the graph of f is the point 0 comma 4 on the y axis. Going leftward from the point 0 comma 4 the graph of f is a line that slants upward, passing through the point negative 2 comma 8. Going rightward from the point 0 comma 4 the graph of f is a line that slants upward, passing through the point 2 comma 8. End of figure description.

2. The figure above shows the graph of the function f defined by f of x = the absolute value of 2x, end absolute value, + 4 for all numbers x. For which of the following functions g defined for all numbers x does the graph of g intersect the graph of f ?

  1. g of x = x minus 2
  2. g of x = x + 3
  3. g of x = 2x minus 2
  4. g of x = 2x + 3
  5. g of x = 3x minus 2

Correct Answer: E

Multiple-choice Questions — Select One or More Answer Choices

These questions are multiple-choice questions that ask the test taker to select one or more answer choices from a list of choices. A question may or may not specify the number of choices to select.

Sample Questions

Select one or more answer choices according to the specific question directions.

If the question does not specify how many answer choices to select, select all that apply.

The correct answer may be just one of the choices or as many as all of the choices, depending on the question.

No credit is given unless you select all of the correct choices and no others.

If the question specifies how many answer choices to select, select exactly that number of choices.

1. Each employee of a certain company is in either Department X or Department Y, and there are more than twice as many employees in Department X as in Department Y. The average (arithmetic mean) salary is $25,000 for the employees in Department X and $35,000 for the employees in Department Y. Which of the following amounts could be the average salary for all of the employees of the company?

Indicate all such amounts.

  1. $26,000
  2. $28,000
  3. $29,000
  4. $30,000
  5. $31,000
  6. $32,000
  7. $34,000

Correct Answer: A and B

2. If f, g, and h are positive integers such that, f is a factor of g, and g is a factor of h, which of the following statements must be true?

Indicate all such statements.

  1. f  is a factor of g squared
  2. f  is a factor of gh.
  3. f  is a factor of h minus g

Correct Answer: A, B and C

Numeric Entry Questions

Questions of this type ask the test taker either to enter the answer as an integer or a decimal in a single answer box or to enter it as a fraction in two separate boxes — one for the numerator and one for the denominator. In the computer-delivered test, the computer mouse and keyboard are used to enter the answer.

Sample Questions

Enter your answer as an integer or a decimal if there is a single answer box OR as a fraction if there are two separate boxes — one for the numerator and one for the denominator.

Equivalent forms of the correct answer, such as 2.5 and 2.50, are all correct. Fractions do not need to be reduced to lowest terms, though you may need to reduce your fraction to fit in the boxes.

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

1. If x = 10 to the power negative 1, what is the value of open parenthesis, x + the fraction 1 over x, close parenthesis, times, open parenthesis, 1 over x, close parenthesis

Answer Box

Correct Answer: 101

2. A university admitted 100 students who transferred from other institutions. Of these students, 34 transferred from two-year community colleges, 25 transferred from private four-year institutions, and the rest transferred from public four-year institutions. If two different students are to be selected at random from the 100 students, what is the probability that both students selected will be students who transferred from two-year community colleges?

Give your answer as a fraction.

Fraction answer boxes

Correct Answer: 17 over 150 (or any equivalent fraction).

Data Interpretation Sets

Data Interpretation questions are grouped together and refer to the same table, graph or other data presentation. These questions ask the test taker to interpret or analyze the given data. The types of questions may be Multiple-choice (both types) or Numeric Entry.

Sample Questions

Questions 1 to 3 are based on the following data.

PERCENT CHANGE IN MONTHLY* VALUE OF INVENTORY
AT SIX BUSINESSES FROM APRIL TO JUNE

The table has 3 columns, and 6 rows.

Business

Percent Change
from April to May

Percent Change
from May to June

G 6 8
K 5 minus 5
M 2 12
R 8 minus 5
V 14 0
Z 2 minus 10

*Inventory values are determined at the end of each month.

1. If the value of the inventory at Business K was $30,000 for April, what was the value of the inventory at Business K for June?

  1. $22,500
  2. $29,925
  3. $30,000
  4. $33,000
  5. $33,075

Correct Answer: B

2.At Business M, the value of the inventory for May was what percent of the value of the inventory for June?

Give your answer to the nearest 0.1 percent.

Answer box followed by percent sign%

Correct Answer: 89.3

3. For which of the six businesses shown was the percent change in the value of the inventory from April to June greatest?

  1. G
  2. K
  3. M
  4. R
  5. V

Correct Answer: A

Questions 4 to 6 are based on the following data.

The title of the data for questions 4-6 is Workforce of Country X. The data consists of a pie chart and a horizontal bar graph. The title of the pie chart is Percent Distribution of Workforce by Employment Sector and the title of the bar graph is Workforce in the Service Sector by Area and Union Membership. The percent distribution of the workforce by employment sector in the pie chart is as follows: Professional Sector 20%. Service Sector 15%. Construction and Maintenance Sector 10%. Production and Transportation Sector 15%. Other Sector 15%. Sales Sector 10%. Management Sector 15%. The bar graph shows the number of union Members and Nonmembers in each of five Service Sector areas. The horizontal axis is labeled Millions of People, with vertical gridlines, from 0 million to 4 million, in increments of 0.5 million, indicated. The vertical axis has five Service Sector areas indicated. The data in the bar graph is as follows: Health Care Area, 0.5 million Members and about 2.75 million Nonmembers. Protective Service Area, a little under 2 million Members and 0.5 million Nonmembers. Food Service Area, a little under 3 million Members and a little under 4 million Nonmembers. Personal Care Area, a little over 0.5 million Members and about 2.75 million Nonmembers. Other Area, a little under 3 million Members and a little under 2 million Nonmembers. End of figure description

4. Approximately how many people are in the production and transportation sector of the workforce?

  1. 9 million
  2. 12 million
  3. 15 million
  4. 18 million
  5. 21 million

Correct Answer: E

5. Approximately what fraction of the workforce in the food service area of the service sector consists of union members?

  1. 1 fourth
  2. 1 third
  3. 3 sevenths
  4. 4 sevenths
  5. 7 tenths

Correct Answer: C

6. In the workforce, the ratio of the number of union members to the number of nonmembers is the same for the sales sector as it is for the protective service area of the service sector. Which of the following is closest to the number of nonmembers in the sales sector?

  1. 2.9 million
  2. 3.6 million
  3. 10.4 million
  4. 11.1 million
  5. 14.0 million

Correct Answer: A

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