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GRE General Test — Quantitative Comparison

36 free practice questions with full explanations.

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Question 1

Quantity A: The number of prime numbers between 1 and 20. Quantity B: 8. Which is greater?

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

Show answer & explanation

Correct answer: C) The two quantities are equal

The primes between 1 and 20 are 2, 3, 5, 7, 11, 13, 17, 19 -- exactly 8 primes, matching Quantity B.

Question 2

0 < a < b. Quantity A: a/b. Quantity B: b/a. Which is greater?

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

Show answer & explanation

Correct answer: B) Quantity B is greater

Since 0 < a < b, a/b is a positive fraction less than 1, while b/a is a positive value greater than 1 (the reciprocal of a fraction less than 1). Since anything greater than 1 exceeds anything less than 1, Quantity B is greater.

Question 3

Quantity A: 7/12. Quantity B: 0.58. Which is greater?

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

Show answer & explanation

Correct answer: A) Quantity A is greater

7/12 ≈ 0.5833, which is greater than 0.58. So Quantity A is greater.

Question 4

x and y are positive integers with x + y = 10. Quantity A: x times y. Quantity B: 24. Which is greater?

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

Show answer & explanation

Correct answer: D) The relationship cannot be determined from the information given

Possible pairs (x,y) with x+y=10: (1,9)->9, (2,8)->16, (3,7)->21, (4,6)->24, (5,5)->25. Products range from 9 to 25 depending on the pair, so the comparison to 24 varies (sometimes less, sometimes equal, sometimes greater). The relationship cannot be determined.

Question 5

Quantity A: The perimeter of an equilateral triangle with side length 8. Quantity B: The perimeter of a square with side length 6. Which is greater?

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

Show answer & explanation

Correct answer: C) The two quantities are equal

Equilateral triangle perimeter = 3 x 8 = 24. Square perimeter = 4 x 6 = 24. Both equal 24.

Question 6

A jar contains 6 red and 9 blue marbles. Quantity A: The probability of drawing a red marble. Quantity B: 2/5.

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

Show answer & explanation

Correct answer: C) The two quantities are equal

P(red)=6/15=2/5=0.4000. Quantity B = 2/5=0.4000. The quantities are equal.

Question 7

Quantity A: The area of a circle with diameter 10. Quantity B: 80.

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

Show answer & explanation

Correct answer: B) Quantity B is greater

Radius=5. Area=pi(25)≈78.54, which is less than 80.

Question 8

x = 4. Quantity A: 3x + 2. Quantity B: 2x + 7.

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

Show answer & explanation

Correct answer: B) Quantity B is greater

Quantity A = 3(4)+2=14. Quantity B = 2(4)+7=15.

Question 9

Quantity A: 5/6. Quantity B: 0.84.

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

Show answer & explanation

Correct answer: B) Quantity B is greater

5/6 = 0.8333, which is less than 0.84.

Question 10

n is a positive integer. Quantity A: (-1)^n. Quantity B: 0.

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

Show answer & explanation

Correct answer: D) The relationship cannot be determined from the information given

If n is even, (-1)^n=1 (A greater). If n is odd, (-1)^n=-1 (B greater). Since n's parity is not specified, the relationship cannot be determined.

Question 11

Quantity A: {(-3)}^4. Quantity B: {-3}^4 (i.e., the negative of 3^4). Which is greater?

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

Show answer & explanation

Correct answer: A) Quantity A is greater

Quantity A: (-3)^4 = 81 (an even power of a negative number is positive). Quantity B: -(3^4) = -81 (the negative sign is applied after exponentiation). Since 81 > -81, Quantity A is greater.

Question 12

The average (arithmetic mean) of 5 consecutive integers is 20. Quantity A: The smallest of the 5 integers. Quantity B: 18. Which is greater?

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

Show answer & explanation

Correct answer: C) The two quantities are equal

For 5 consecutive integers, the mean equals the middle (3rd) value, so the integers are 18, 19, 20, 21, 22. The smallest is 18, which equals Quantity B.

Question 13

Quantity A: 3/7. Quantity B: 0.43. Which is greater?

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

Show answer & explanation

Correct answer: B) Quantity B is greater

3/7 ≈ 0.4286, which is less than 0.43. So Quantity B is greater.

Question 14

x is a positive integer. Quantity A: x^2. Quantity B: 2x. Which is greater?

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

Show answer & explanation

Correct answer: D) The relationship cannot be determined from the information given

If x = 1: A=1, B=2, B is greater. If x = 2: A=4, B=4, equal. If x = 3: A=9, B=6, A is greater. Since the relationship changes depending on the value of x, it cannot be determined.

Question 15

Quantity A: The area of a circle with radius 4. Quantity B: The area of a square with side 6. Which is greater?

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

Show answer & explanation

Correct answer: A) Quantity A is greater

Quantity A = pi x r^2 = pi x 16 ≈ 50.27. Quantity B = 6^2 = 36. Since 50.27 > 36, Quantity A is greater.

Question 16

x > 0. Quantity A: x/(x+1). Quantity B: (x+1)/(x+2). Which is greater?

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

Show answer & explanation

Correct answer: B) Quantity B is greater

Cross-multiplying (valid since x>0, all terms positive): compare x(x+2) vs (x+1)(x+1). x^2+2x vs x^2+2x+1. The second is always 1 greater, so (x+1)/(x+2) > x/(x+1) for all x > 0. Quantity B is greater.

Question 17

Quantity A: 5/9. Quantity B: 0.56. Which is greater?

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

Show answer & explanation

Correct answer: B) Quantity B is greater

5/9 ≈ 0.5556, which is less than 0.56. So Quantity B is greater.

Question 18

x < 0. Quantity A: x^3. Quantity B: x^2. Which is greater?

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

Show answer & explanation

Correct answer: B) Quantity B is greater

For any negative x, x^3 is negative (odd power preserves sign) while x^2 is always positive (even power). A positive number is always greater than a negative number, so Quantity B (x^2, positive) is always greater than Quantity A (x^3, negative).

Question 19

A rectangle has length 12 and width 5. Quantity A: The area of the rectangle. Quantity B: The perimeter of the rectangle multiplied by 2. Which is greater?

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

Show answer & explanation

Correct answer: B) Quantity B is greater

Area = 12 x 5 = 60. Perimeter = 2(12+5) = 34, and Perimeter x 2 = 68. Since 68 > 60, Quantity B is greater.

Question 20

n is an integer and 2 < n < 8. Quantity A: The number of possible values of n. Quantity B: 5. Which is greater?

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

Show answer & explanation

Correct answer: C) The two quantities are equal

The integers strictly between 2 and 8 are 3, 4, 5, 6, 7 -- exactly 5 values. Quantity A equals 5, matching Quantity B.

Question 21

Quantity A: The average (arithmetic mean) of 8, 12, and 22. Quantity B: The median of 8, 12, and 22. Which is greater?

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

Show answer & explanation

Correct answer: A) Quantity A is greater

Mean = (8+12+22)/3 = 42/3 = 14. Median (middle value) = 12. Since 14 > 12, Quantity A is greater.

Question 22

Quantity A: 9/16. Quantity B: 0.55. Which is greater?

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

Show answer & explanation

Correct answer: A) Quantity A is greater

9/16 = 0.5625, which is greater than 0.55. So Quantity A is greater.

Question 23

x is an integer such that x^2 < 50. Quantity A: The greatest possible value of x. Quantity B: 7. Which is greater?

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

Show answer & explanation

Correct answer: C) The two quantities are equal

7^2 = 49 < 50, so x=7 satisfies the constraint. 8^2 = 64 > 50, so x cannot be 8 or greater. The greatest possible value of x is 7, matching Quantity B exactly.

Question 24

In triangle ABC, angle A = 90 degrees. Quantity A: angle B + angle C. Quantity B: 90 degrees. Which is greater?

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

Show answer & explanation

Correct answer: C) The two quantities are equal

The angles of a triangle sum to 180 degrees. Since angle A = 90, angle B + angle C = 180 - 90 = 90 degrees, exactly matching Quantity B.

Question 25

Quantity A: The number of positive integer factors of 100. Quantity B: The number of positive integer factors of 64. Which is greater?

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

Show answer & explanation

Correct answer: A) Quantity A is greater

100 = 2^2 x 5^2, giving (2+1)(2+1) = 9 factors. 64 = 2^6, giving (6+1) = 7 factors. Since 9 > 7, Quantity A is greater.

Question 26

Quantity A: The average (arithmetic mean) of the first 10 positive integers. Quantity B: The median of the first 10 positive integers. Which is greater?

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

Show answer & explanation

Correct answer: C) The two quantities are equal

The first 10 positive integers (1 through 10) are evenly spaced. Mean = (1+10)/2 = 5.5. Median = average of 5th and 6th values = (5+6)/2 = 5.5. Both equal 5.5.

Question 27

y = |x - 3| Quantity A: y when x = 1 Quantity B: y when x = 8

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
E) Quantity A equals 5

Show answer & explanation

Correct answer: B) Quantity B is greater

At x = 1: y = |1-3| = 2. At x = 8: y = |8-3| = 5. Since 5 > 2, Quantity B is greater.

Question 28

Quantity A: The value of x if 3x + 7 = 28 Quantity B: 6

A) Quantity B is greater
B) The two quantities are equal
C) Quantity A is greater
D) The relationship cannot be determined from the information given
E) Quantity A equals exactly 5

Show answer & explanation

Correct answer: C) Quantity A is greater

3x + 7 = 28 -> 3x = 21 -> x = 7. Since 7 > 6, Quantity A is greater.

Question 29

x > 0 Quantity A: x^2 Quantity B: x^3

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
E) Quantity A is always negative

Show answer & explanation

Correct answer: D) The relationship cannot be determined from the information given

If 0 < x < 1 (e.g., x = 0.5), x^2 > x^3. If x > 1 (e.g., x = 2), x^3 > x^2. If x = 1, they're equal. Since x can be any positive number, the relationship varies -- cannot be determined.

Question 30

Set S consists of the integers from 10 to 50, inclusive. Quantity A: The number of integers in Set S Quantity B: 41

A) Quantity A is greater
B) Quantity B is greater
C) The relationship cannot be determined from the information given
D) Quantity A equals 40
E) The two quantities are equal

Show answer & explanation

Correct answer: E) The two quantities are equal

Count of integers from 10 to 50 inclusive = 50 - 10 + 1 = 41. Quantity A equals Quantity B exactly.

Question 31

A rectangle has a perimeter of 24. Quantity A: The maximum possible area of the rectangle Quantity B: 36

A) The two quantities are equal
B) Quantity A is greater
C) Quantity B is greater
D) The relationship cannot be determined from the information given
E) Quantity A is exactly 24

Show answer & explanation

Correct answer: A) The two quantities are equal

For a fixed perimeter, area is maximized when the rectangle is a square. Perimeter 24 -> each side = 6 -> area = 36. Quantity A's maximum equals Quantity B.

Question 32

Quantity A: 8/9. Quantity B: 0.87.

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

Show answer & explanation

Correct answer: C) Quantity A is greater

8/9 = 0.8889 (approximately), which is greater than 0.87. So Quantity A is greater.

Question 33

A jar contains 9 red and 6 blue marbles. Quantity A: The probability of drawing a blue marble. Quantity B: 3/7.

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

Show answer & explanation

Correct answer: A) Quantity B is greater

Total marbles = 9+6=15. P(blue) = 6/15 = 2/5 = 0.4000. Quantity B = 3/7 ≈ 0.4286. Since 0.4286 > 0.4, Quantity B is greater.

Question 34

n is a positive integer. Quantity A: n^2. Quantity B: 3n.

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

Show answer & explanation

Correct answer: D) The relationship cannot be determined from the information given

If n=1: n^2=1, 3n=3 (B greater). If n=3: n^2=9, 3n=9 (equal). If n=4: n^2=16, 3n=12 (A greater). Since the relationship changes depending on n, it cannot be determined.

Question 35

A rectangle has a perimeter of 28. Quantity A: The maximum possible area of the rectangle. Quantity B: 49.

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

Show answer & explanation

Correct answer: B) The two quantities are equal

For a fixed perimeter, area is maximized when the rectangle is a square. Perimeter 28 -> each side = 7 -> area = 49. Quantity A's maximum equals Quantity B.

Question 36

x = 3. Quantity A: 2x + 5. Quantity B: 5x - 2.

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

Show answer & explanation

Correct answer: A) Quantity B is greater

Quantity A = 2(3)+5 = 11. Quantity B = 5(3)-2 = 13. Since 13 > 11, Quantity B is greater.

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