Full GRE practice test

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GRE Quantitative Reasoning practice: section 2 (harder)

15 harder questions across arithmetic, algebra, geometry and data analysis, with a three-question data set. Same number of questions and time limit as the real GRE Quant 2.

All questions are written by Keiko Study in the official format; they are not official GRE papers.

Take the GRE Quant 2 section

15 questions, 26 minutes. Start the timer for real exam conditions, or answer at your own pace. When you submit, you get your score, the correct answers and a worked solution for every question.

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Question 1

Remainders

When the positive integer $n$ is divided by 6, the remainder is 4.

Compare Quantity A and Quantity B.

Quantity A	Quantity B
The remainder when $n^{2}$ is divided by 6	$4$

Quantity A is greater.Quantity B is greater.The two quantities are equal.The relationship cannot be determined from the information given.

Question 2

Inequalities with powers

The number $x$ satisfies $x^{2} < ∣ x ∣$ .

Compare Quantity A and Quantity B.

Quantity A	Quantity B
$x$	$x^{3}$

Quantity A is greater.Quantity B is greater.The two quantities are equal.The relationship cannot be determined from the information given.

Question 3

Greatest common divisor and least common multiple

$x$ and $y$ are positive integers. The greatest common divisor of $x$ and $y$ is 6, and their least common multiple is 180.

Compare Quantity A and Quantity B.

Quantity A	Quantity B
$x + y$	$66$

Quantity A is greater.Quantity B is greater.The two quantities are equal.The relationship cannot be determined from the information given.

Question 4

Triangle area

A triangle has sides of lengths 7, 10 and 12.

Compare Quantity A and Quantity B.

Quantity A	Quantity B
The area of the triangle	$35$

Quantity A is greater.Quantity B is greater.The two quantities are equal.The relationship cannot be determined from the information given.

Question 5

Normal distribution and quartiles

The scores of a large group of students on a test are approximately normally distributed, with a mean of 150 and a standard deviation of 10.

Compare Quantity A and Quantity B.

Quantity A	Quantity B
The third quartile of the scores	$160$

Quantity A is greater.Quantity B is greater.The two quantities are equal.The relationship cannot be determined from the information given.

Question 6

Algebraic identities

If $\frac{1}{x} + \frac{1}{y} = \frac{1}{4}$ and $x + y = 25$ , what is the value of $(x - y)^{2}$ ?

Question 7

Absolute value inequalities

Which of the following values of $x$ satisfy the inequality $∣ 2 x - 3 ∣ < x + 1$ ?

Indicate all such values.

Select all the answer choices that apply.

Question 8

Probability

Two different integers are chosen at random from the integers 1 through 10, inclusive. What is the probability that the product of the two integers is a multiple of 3?

Give your answer as a fraction.

Enter your answer as a whole number, a decimal or a fraction such as 3/4.

Questions 9–11

Bicycle sales by type, 2020–2024

A bicycle manufacturer sells four types of bicycle. The table shows the total number of bicycles it sold in each year from 2020 to 2024, and the percent of that year's total accounted for by each type.

Year	Total sold (thousands)	Road	Mountain	Electric	Children's
2020	80	35%	30%	10%	25%
2021	96	30%	30%	15%	25%
2022	100	28%	26%	25%	21%
2023	120	26%	25%	30%	19%
2024	125	24%	22%	36%	18%

Question 9

Data interpretation: percents of a total

In which year did the manufacturer sell the greatest number of mountain bicycles?

Question 10

Data interpretation: percent change

By what percent did the number of children's bicycles sold increase from 2020 to 2024?

Enter your answer as a whole number, a decimal or a fraction such as 3/4.

%

Question 11

Data interpretation: weighted averages

Of all the bicycles the manufacturer sold from 2020 to 2024, inclusive, approximately what percent were electric bicycles?

Question 12

Similar right triangles

In triangle $A B C$ , angle $C$ is a right angle. Point $D$ lies on side $A B$ , and segment $C D$ is perpendicular to $A B$ . If $A D = 4$ and $D B = 9$ , what is the area of triangle $A B C$ ?

Question 13

Work rates

Working together at their respective constant rates, Aiko and Bilal can paint a fence in 4 hours. Working alone, Aiko takes 6 hours longer than Bilal to paint the fence. How many hours does Aiko take to paint the fence alone?

Question 14

Standard deviation

Each option below describes a change to the list of numbers 10, 20, 30, 40, 50. Which of the changes, made on its own, would increase the standard deviation of the list?

Indicate all such changes.

Select all the answer choices that apply.

Add the number 30 to the list.Remove the number 30 from the list.Add 5 to every number in the list.Multiply every number in the list by

- 2

.Replace 20 with 25, and replace 40 with 35.Add the numbers 0 and 60 to the list.

Question 15

Counting with inclusion–exclusion

A security code consists of 4 digits, each chosen from 0 through 9. Digits may repeat, and a code may begin with 0. How many different codes contain at least one 0 and at least one 7?

0 of 15 answered