GRE Quantitative Comparison Practice Test 2
- Quantitative Comparison (Set 2)
- 10 questions
- 12 minutes
Each question asks you to compare Quantity A with Quantity B using the same four answer choices as the real GRE. Choose "cannot be determined" only after you have found two allowed cases that point in different directions.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
x > 0
Quantity A Quantity B (x + 1)² x² + 1 Compare Quantity A and Quantity B.
Correct answer: A
Expanding, (x + 1)² = x² + 2x + 1, which is 2x more than Quantity B. Since x is positive, 2x > 0 and Quantity A is always greater.
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Question 2
n is a positive odd integer.
Quantity A Quantity B The remainder when n² is divided by 8 1 Compare Quantity A and Quantity B.
Correct answer: C
Write n = 2m + 1. Then n² = 4m(m + 1) + 1, and m(m + 1) is even, so 4m(m + 1) is a multiple of 8. The remainder is always 1, for example 9 = 8 + 1 and 49 = 48 + 1.
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Question 3
The price of a jacket is $100. The price is increased by 20%, and then the new price is decreased by 20%.
Quantity A Quantity B The final price, in dollars 100 Compare Quantity A and Quantity B.
Correct answer: B
After the increase the price is $120, and 20% of $120 is $24, so the final price is $96. The decrease is taken from a larger base than the increase, so the two changes do not cancel.
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Question 4
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: for x = 0.25 the square root is 0.5. In general x = x × x and x < 1, so x < x.
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Question 5
xy ≠ 0 and x² = y²
Quantity A Quantity B x y Compare Quantity A and Quantity B.
Correct answer: D
x² = y² means x = y or x = −y. With x = y = 2 the quantities are equal, but with x = 2 and y = −2 Quantity A is greater, so the relationship cannot be determined.
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Question 6
The data set is 2, 4, 4, 9, 16.
Quantity A Quantity B The arithmetic mean of the data set The median of the data set Compare Quantity A and Quantity B.
Correct answer: A
The sum is 35, so the mean is 35 ÷ 5 = 7. The median is the middle value of the ordered list, 4. The large value 16 pulls the mean above the median.
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Question 7
A triangle has sides of length 5, 12 and x, and the angle opposite the side of length x is greater than 90°.
Quantity A Quantity B x 13 Compare Quantity A and Quantity B.
Correct answer: A
If that angle were exactly 90°, x would be 13 because 5² + 12² = 169 = 13². An obtuse angle opposite a side makes that side longer than in the right triangle, so x² > 169 and x > 13.
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Question 8
k is an integer and 3 < k < 7.
Quantity A Quantity B The number of positive divisors of k 3 Compare Quantity A and Quantity B.
Correct answer: D
k can be 4, 5 or 6. The number 4 has 3 divisors (1, 2, 4), 5 has only 2, and 6 has 4 (1, 2, 3, 6). Depending on k, Quantity A can be equal to, less than or greater than 3.
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Question 9
Quantity A Quantity B 230 + 230 231 Compare Quantity A and Quantity B.
Correct answer: C
Adding two equal powers doubles one of them: 230 + 230 = 2 × 230 = 231. A common trap is to add the exponents and get 260.
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Question 10
A circle has a circumference of 10π.
Quantity A Quantity B The area of the circle 80 Compare Quantity A and Quantity B.
Correct answer: B
A circumference of 10π means the radius is 5, so the area is 25π. Since π is about 3.14, 25π is about 78.5, which is less than 80.
Questions you leave blank are not counted as wrong.
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