Official GRE Quantitative Reasoning

GRADUATE RECORD EXAMINATIONS®

Official G R E Quantitative Reasoning Practice Questions, Volume 1

Chapter 3 – Arithmetic Questions

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0ea741df731652e502ac69350f1f4177.doc Page 1 Chapter 3

Arithmetic

This chapter contains G R E Quantitative Reasoning practice questions that involve arithmetic.

Arithmetic topics include properties and types of integers, such as divisibility, factorization, prime numbers, remainders, and odd and even integers; arithmetic operations, exponents, and roots; and concepts such as estimation, percent, ratio, rate, absolute value, the number line, decimal representation, and sequences of numbers.

The questions are arranged by question type: Quantitative Comparison questions, followed by both types of Multiple-choice questions, and then Numeric Entry questions.

The answer key and the explanations for the answers for the Arithmetic Questions are in the

separate document named “G R E Chapter 3 Arithmetic Answers and Explanations.doc.”

Review the answers and explanations carefully, paying particular attention to explanations for questions that you answered incorrectly.

Before answering the practice questions, read the Quantitative Reasoning section directions that begin on the next page. Also, review the directions that precede each question type to make sure you understand how to answer the questions.

0ea741df731652e502ac69350f1f4177.doc Page 2 Quantitative Reasoning Section Directions

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.

0ea741df731652e502ac69350f1f4177.doc Page 3 Quantitative Comparison Questions For Questions 1 to 7, 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. (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

0ea741df731652e502ac69350f1f4177.doc Page 4 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.

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.

Question 1.

It is given that D is the decimal form of the fraction 4 over 11.

Quantity A: The 25th digit to the right of the decimal point in D

Quantity B: 4

A. Quantity A is greater.

B. Quantity B is greater.

C. The two quantities are equal.

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.

0ea741df731652e502ac69350f1f4177.doc Page 5 Question 2.

Quantity A: The cube root of 270, minus, the cube root of 10

Quantity B: The cube root of 80

Question 3.

It is given that n is a positive integer, x = 7n + 2, and y = 6n + 3.

Quantity A: The ones digit of x + y

Quantity B: 5

It is given that r = 2 and s = negative 7.

Quantity A: open parenthesis, r minus s, close parenthesis, raised to the 4th power

Quantity B: r raised to the 4th power, minus, s raised to the 4th power

Question 5.

It is given that n is an even negative integer.

Quantity A: one third, raised to the n power

Quantity B: open parenthesis, negative 3, close parenthesis, raised to the n power

Today the price of a table was reduced by 20 percent from what it was yesterday, and the price of a lamp was reduced by 30 percent from what it was yesterday.

Quantity A: The dollar amount of the reduction in the price of the table

Quantity B: The dollar amount of the reduction in the price of the lamp

Question 7.

For 5 hours, a photocopier copied at a constant rate of 2 pages every 3 seconds.

Quantity A: The number of pages the photocopier copied in the 5 hours

Quantity B: 12,000

0ea741df731652e502ac69350f1f4177.doc Page 8 Multiple-choice Questions—Select One Answer Choice

Question 8.

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

For each integer n greater than 1, let A of n denote the sum of the integers from 1 to n. For example, A of 100 = 1 + 2 + 3 + dot, dot, dot, + 100, which is equal to 5,050. What is the value of A of 200 ?

A 10,100

B 15,050

C 15,150

D 20,100

E 21,500

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

Question 9.

Which of the following integers CANNOT be expressed as the sum of two prime numbers?

When the positive integer n is divided by 45, the remainder is 18. Which of the following must be a divisor of n ?

Question 11.

Refer to the figure.

Figure for Arithmetic Question 11

The figure shows four points on a number line. From left to right, the four points are point A, point B, point C, and point D.

0ea741df731652e502ac69350f1f4177.doc Page 10 Begin skippable part of figure description.

The coordinate of point A is one third, and the coordinate of point D is one half. Points B and C divide line segment AD into 3 smaller line segments AB, BC, and CD.

End skippable part of figure description.

Points A, B, C, and D are on the number line above, and the length of AB is equal to the length of CD, which is equal to one third of the length of BC. What is the coordinate of C ?

A. the fraction 13 over 30

B. the fraction 9 over 20

C. the fraction 11 over 24

D. the fraction 7 over 15

E. the fraction 29 over 60

Which of the following represents the total dollar amount that a customer would have to pay for an item that costs s dollars plus a sales tax of 8 percent, in terms of s ?

A. the fraction s over 0.08

B. the fraction s over 1.08

C. the fraction s over 8

D. 0.08s

E. 1.08s

Question 13.

Marie earned $0.75 for every mile she walked in a charity walkathon. If she earned a total of $18.00 at that rate, how many miles did she walk?

A. 13.5

B. 17.5

D. 22.5

0ea741df731652e502ac69350f1f4177.doc Page 12 Select and indicate the best one of the answer choices given.

0ea741df731652e502ac69350f1f4177.doc Page 13 Multiple-choice Questions—Select One or More Answer Choices

Question 14.

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

Which of the following operations carried out on both the numerator and the denominator of a fraction will always produce an equivalent fraction?

Indicate all such numbers.

A. Adding 2

B. Multiplying by 5

C. Dividing by 100

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.

Question 15.

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

If the absolute value of z is less than or equal to 1, which of the following statements must be true?

Indicate all such statements.

A. z squared is less than or equal to 1.

B. z squared is less than or equal to z.

C. z cubed is less than or equal to z.

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.

This question has eight answer choices, labeled A through H. Select all the answer choices that apply.

In a certain medical group, Doctor Schwartz schedules appointments to begin 30 minutes apart, Doctor Ramirez schedules appointments to begin 25 minutes apart, and Doctor Wu schedules appointments to begin 50 minutes apart. All three doctors schedule their first appointments to begin at 8:00 in the morning, which are followed by their successive appointments throughout the day without breaks. Other than at 8:00 in the morning, at what times before 1:30 in the afternoon do all three doctors schedule their appointments to begin at the same time?

Indicate all such times.

A. 9:30 in the morning

B. 10:00 in the morning

C. 10:30 in the morning

D. 11:00 in the morning

E. 11:30 in the morning

F. 12:00 noon

G. 12:30 in the afternoon

H. 1:00 in the afternoon

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 eight of the answer choices.

0ea741df731652e502ac69350f1f4177.doc Page 15 Numeric Entry Questions Questions 17 to 19 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 marking entries in the grid in steps 5 and 6, you will be asked to circle those entries.

Question 17. 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.

The integers x and y are greater than 1. If 4 x times 7 y = 756, what is the value of x + y ?

0ea741df731652e502ac69350f1f4177.doc Page 16 The answer space is preceded by the label “x + y =.”

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.

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.

In the sequence 1, negative 3, 4, 1, negative 3, 4, 1, negative 3, 4, dot, dot, dot, the first 3 terms repeat without end. What is the sum of the terms of the sequence from the 150th term to the 154th term?

Question 19.

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.

A manufacturing company has plants in three locations: Indonesia, Mexico, and Pakistan. The company has 6,000 employees, and each of the employees works at only one of the plants. If three eighths of the employees work at the plant in Indonesia and if twice as many employees work at the plant in Mexico as work at the plant in Pakistan, how many employees work at the plant in Mexico?

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

The answer key and the explanations for the answers for the Arithmetic Questions are in the separate document titled “GRE Chapter 3 – Arithmetic Answers and Explanations.doc.”

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