GRE Quantitative Reasoning practice: section 1

Question 1

Fractions and averages

Compare Quantity A and Quantity B.

Quantity A	Quantity B
$\frac{1}{4}$	The average (arithmetic mean) of $\frac{1}{3}$ and $\frac{1}{5}$

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 and reciprocals

$a$ and $b$ are nonzero numbers, and $a > b$ .

Compare Quantity A and Quantity B.

Quantity A	Quantity B
$\frac{1}{a}$	$\frac{1}{b}$

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

Question 3

Circles and right triangles

Triangle $A B C$ is inscribed in a circle, so all three of its vertices lie on the circle. Angle $C$ is a right angle, $A C = 6$ , and $B C = 8$ .

Compare Quantity A and Quantity B.

Quantity A	Quantity B
The area of the circle	$25 π$

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

Question 4

Median and mean

A list consists of five numbers. The median of the five numbers is 10, and their average (arithmetic mean) is 12.

Compare Quantity A and Quantity B.

Quantity A	Quantity B
The greatest number in the list	14

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

Question 5

Linear equations in word problems

Priya bought 14 items at a stationery shop: some notebooks at $3.00 each, and the rest pens at $1.50 each. She spent $30.00 in total. How many notebooks did she buy?

Question 6

Volume and surface area

A closed rectangular box has a square base and a height of 6 centimeters. If the volume of the box is 150 cubic centimeters, what is the total surface area of the box, in square centimeters?

Question 7

Successive percent changes

A shop raised the price of a lamp by 20%. Later, it reduced the new price by 15%, and the lamp then sold for $51. What was the price of the lamp, in dollars, before the 20% increase?

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

Questions 8–9

International students at a university

The table shows the number of international students enrolled at a university in 2024 and in 2025, by home region. Each international student is counted in exactly one region.

Home region	2024	2025
Africa	300	360
East Asia	1,240	1,282
Europe	520	494
Latin America	240	312
South Asia	900	1,152
Total	3,200	3,600

Question 8

Data interpretation: percent change

For which home region was the percent increase in the number of international students from 2024 to 2025 the greatest?

Question 9

Data interpretation: projections

Suppose the total number of international students at the university increases by the same percent from 2025 to 2026 as it did from 2024 to 2025. How many international students will the university have in 2026?

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

Question 10

Divisibility and prime factors

If $n$ is a positive integer and $n^{2}$ is divisible by 72, which of the following integers must be divisors of $n$ ?

Indicate all such integers.

Select all the answer choices that apply.

Question 11

Coordinate geometry: lines

In the $x y$ -plane, line $k$ passes through the points $(- 2, 3)$ and $(4, - 1)$ . What is the $y$ -intercept of line $k$ ?

Question 12

Probability and counting

Ayumi, Bilal and Carmen each choose a whole number from 1 to 4. Each person chooses at random and independently of the others, with all four numbers equally likely, so two or more people may choose the same number. What is the probability that the greatest of the three numbers chosen is exactly 3?

Take the GRE Quant 1 section

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

International students at a university

Question 8

Question 9

Question 10

Question 11

Question 12