GRE Quantitative Reasoning Practice: Quantitative Comparison
- Quantitative Comparison
- 15 questions
- 26 minutes
Quantitative Comparison is one of the four question types in GRE Quantitative Reasoning, and every item has the same four answer choices. Before calculating, test special values such as 0, 1, a negative number and a fraction: if two allowed values give different results, the answer is "cannot be determined." The 26-minute limit matches the second Quantitative section of the current test (15 questions).
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Question 1
x is a negative integer.
Quantity A Quantity B x² x³ Compare Quantity A and Quantity B.
Correct answer: A
A negative number squared is positive and a negative number cubed is negative. So x² > 0 > x³ for every negative integer, and Quantity A is always greater.
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Question 2
Quantity A Quantity B 38 of 64 512 of 60 Compare Quantity A and Quantity B.
Correct answer: B
Quantity A is 64 ÷ 8 · 3 = 24 and Quantity B is 60 ÷ 12 · 5 = 25, so Quantity B is greater.
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Question 3
Quantity A Quantity B The number of distinct prime factors of 210 The number of distinct prime factors of 1,155 Compare Quantity A and Quantity B.
Correct answer: C
210 = 2 · 3 · 5 · 7 and 1,155 = 3 · 5 · 7 · 11. Each number has exactly 4 distinct prime factors, so the quantities are equal.
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Question 4
p is a prime number and 3 < p < 12.
Quantity A Quantity B p 7 Compare Quantity A and Quantity B.
Correct answer: D
The primes between 3 and 12 are 5, 7 and 11. If p = 5, Quantity B is greater; if p = 11, Quantity A is greater. Because both can happen, the relationship cannot be determined.
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Question 5
Two sides of a triangle have lengths 7 and 10.
Quantity A Quantity B The length of the third side 17 Compare Quantity A and Quantity B.
Correct answer: B
By the triangle inequality, the third side must be less than 7 + 10 = 17 (and greater than 3). So Quantity B is always greater.
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Question 6
Quantity A Quantity B 210 103 Compare Quantity A and Quantity B.
Correct answer: A
210 = 1,024 and 103 = 1,000, so Quantity A is greater, although only slightly.
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Question 7
k is an integer.
Quantity A Quantity B The average (arithmetic mean) of k, k + 1, k + 2, k + 3 and k + 4 k + 2 Compare Quantity A and Quantity B.
Correct answer: C
The sum is 5k + 10, and dividing by 5 gives k + 2. For any evenly spaced list, the average is the middle term, so the quantities are equal.
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Question 8
0 < x < 1
Quantity A Quantity B x x Compare Quantity A and Quantity B.
Correct answer: B
For a number between 0 and 1, the square root is larger than the number itself: for example, 0.25 = 0.5. Since 0 < x < 1 means x² < x, taking square roots gives x < x.
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Question 9
x + y = 10
Quantity A Quantity B xy 25 Compare Quantity A and Quantity B.
Correct answer: D
If x = y = 5, then xy = 25 and the quantities are equal. If x = 2 and y = 8, then xy = 16, which is less. Two different relationships are possible, so it cannot be determined.
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Question 10
Quantity A Quantity B The percent increase from 40 to 50 The percent decrease from 50 to 40 Compare Quantity A and Quantity B.
Correct answer: A
Both changes are 10, but the increase is measured from 40 (10/40 = 25%) and the decrease from 50 (10/50 = 20%). Quantity A is greater.
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Question 11
Quantity A Quantity B The circumference of a circle with diameter 7 The perimeter of a square with side length 5.5 Compare Quantity A and Quantity B.
Correct answer: B
The circumference is 7π ≈ 21.99 and the perimeter is 4 · 5.5 = 22. Quantity B is greater by a small margin; using π ≈ 22/7 here would wrongly make them look equal.
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Question 12
Quantity A Quantity B 12 · 3 6 Compare Quantity A and Quantity B.
Correct answer: C
12 · 3 = 36 = 6, so the quantities are equal.
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Question 13
x > y > 0
Quantity A Quantity B xy x + 1y + 1 Compare Quantity A and Quantity B.
Correct answer: A
The difference is x/y − (x + 1)/(y + 1) = (x − y)/(y(y + 1)), which is positive when x > y > 0. For example, 2/1 = 2 is greater than 3/2.
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Question 14
a and b are nonzero numbers.
Quantity A Quantity B (a + b)² a² + b² Compare Quantity A and Quantity B.
Correct answer: D
(a + b)² = a² + 2ab + b², so the comparison depends on the sign of ab. If a = b = 1, Quantity A is greater; if a = 1 and b = −1, Quantity B is greater.
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Question 15
Quantity A Quantity B 15% of 80 80% of 15 Compare Quantity A and Quantity B.
Correct answer: C
Both equal 0.15 · 80 = 0.80 · 15 = 12, because a% of b always equals b% of a.
Questions you leave blank are not counted as wrong.
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