GRE Test Exam Questions and Answers

QUESTION: 25

Quantity A
The average (arithmetic mean) of the length and the width of a rectangle whose perimeter is 18

Quantity B

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

Answer(s): B

Explanation:

The perimeter P of a rectangle is given by the formula:
P = 2 × (length + width)
We are told that the perimeter is 18, so:
18 = 2 × (length + width)
length + width = 9
Quantity A asks for the average (arithmetic mean) of the length and the width, which is:

4.5 (Quantity A) < 5 (Quantity B)

Reveal Solution Next Question

QUESTION: 26

x-1y-1 > 0

Quantity A

Quantity B

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

Answer(s): D

Explanation:

This inequality implies that the product of the reciprocals of x and y is positive. This means both x-1 and y-1 must either both be positive or both be negative. In other words, x and y must have the same sign, meaning both x > 0 and y > 0, or both x < 0 and y < 0.
Quantity A

Quantity B

Since x and y have the same sign, we know that both quantities are positive, but we cannot definitively say which one is greater without knowing the exact values of x and y.

Reveal Solution Next Question

QUESTION: 27

According to a certain model, the number of residents in City W, in thousands of people, n years from the present will be

0.1n2 + 20n + 1,000

Quantity A
The number of residents in City W 10 years from the present, according to the model

Quantity B

1,200,000

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

Answer(s): A

Explanation:

Substitute n = 10 into the formula:
Number of residents = 0.1(10)2 + 20(10) + 1,000.
Number of residents = 10 + 200 + 1,000 = 1,210.
This means the number of residents 10 years from the present is 1,210 thousand, or 1,210,000 people.
1,210,000 > 1,200,000

Reveal Solution Next Question

QUESTION: 28

Line l in the xy-plane contains the points (a, 0) and (0, 6), where b < a < 0.

Quantity A
The slope of line l

Quantity B
-1

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

Answer(s): A

Explanation:

The formula for the slope of a line passing through two points (x1,y1) and (x2,y2) is:

For the points (a,0) and (0,6), the slope is:

We are given that b < a < 0, which means a is a negative number.
Since a is negative, the slope will be positive because dividing by a negative number changes the sign.
Now, we compare this slope with Quantity B, which is -1. The slope is positive and the magnitude of a is less than 6, implying a value greater than 1 for the slope.

Reveal Solution Next Question

QUESTION: 29

Polygon P has n sides (n > 4).

Quantity A
180 more than the sum of the degree measures of the interior angles of P

Quantity B
The sum of the degree measures of the interior angles of a polygon with n + 1 sides

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

Answer(s): C

Explanation:

The sum of the interior angles of a polygon with n sides is given by the formula:
Sum of interior angles = 180(n - 2).
Quantity A asks for 180 more than the sum of the interior angles of polygon P, which has n sides. Using the formula for the sum of the interior angles, we get:
Quantity A = 180(n - 2) + 180 = 180n - 360 + 180 = 180n - 180.
Quantity B is the sum of the interior angles of a polygon with n + 1 sides. Using the formula for the sum of the interior angles for a polygon with n + 1 sides:
Quantity B = 180((n + 1) - 2) = 180(n - 1) = 180n - 180.

Reveal Solution Next Question

QUESTION: 30

Of the 200 integers in a set, the 65th percentile is 20.

Quantity A
The arithmetic mean of the integers in the set

Quantity B
20

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

Answer(s): D

Explanation:

The 65th percentile of a set means that 65% of the numbers in the set are less than or equal to the given value, which in this case is 20. This means that 130 out of the 200 integers in the set are less than or equal to 20, while the remaining 70 integers are greater than or equal to 20.
Understanding Quantity A
The arithmetic mean of a set is the sum of all numbers divided by the total number of numbers. The 65th percentile tells us how many numbers are above and below 20 but does not provide information about the actual values of those numbers. The mean depends on the distribution of all values in the set, and we do not have enough information to determine whether the mean is greater than, less than, or equal to 20.
Compare with Quantity B
Since we do not have the full distribution of numbers in the set, we cannot determine if the mean is greater than, less than, or equal to 20. For example, if the numbers above 20 are much larger, the mean could be greater than 20. If the numbers are more evenly spread, the mean could be equal to or less than 20.
Because the relationship between the mean and 20 depends on the distribution of the numbers, we do not have enough information to determine that relationship.

Reveal Solution Next Question

QUESTION: 31

Quantity A

Quantity B
2-54

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

Answer(s): C

Explanation:

227 - 224 = 224(23 - 1) = 224(8 - 1) = 224 × 7
827 = (23)27 = 281
826 = (23)26 = 278
281 - 278 = 278(23 - 1) = 278(8 - 1) = 278 × 7

224-78 = 2-54

Reveal Solution Next Question

QUESTION: 32

The sum of -5 and k equals m2.

Quantity A
k

Quantity B
4

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

Answer(s): D

Explanation:

-5 + k = m2
k = m2 + 5
m2 + 5 vs 4
m2 + 5 > 4 m2 > -1
Since m2 is always non-negative (because it is a square of a real number), we always have:
m2 0
k = m2 + 5 5
Since k 5, it' is possible that k > 4, but we cannot conclude if k is always greater that 4 without knowing specific values for m.

Reveal Solution Next Question

GRE GRE Test Exam (page: 4) GRE Graduate Record Examination Test: Verbal, Quantitative, Analytical Writing Updated on: 12-Feb-2026

QUESTION: 25

Explanation:

QUESTION: 26

Explanation:

QUESTION: 27

Explanation:

QUESTION: 28

Explanation:

QUESTION: 29

Explanation:

QUESTION: 30

Explanation:

QUESTION: 31

Explanation:

QUESTION: 32

Explanation:

GRE GRE Test Exam (page: 4)
GRE Graduate Record Examination Test: Verbal, Quantitative, Analytical Writing
Updated on: 12-Feb-2026