GRE Quantitative: GRE Quantitative Comparison Practice Questions
Test yourself on GRE Quantitative Comparison with 10 original GRE practice questions. Pick an answer to see instant feedback and a full explanation.
Free original practice questions for study purposes. Open Exam Prep is an independent study resource and is not affiliated with, endorsed by, or sponsored by the makers of GRE.
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Answer the questions below — you get instant feedback and a full explanation for each.
1. Quantity A: x² Quantity B: x, where x is a real number. Which statement is correct?
Explanation. Test values. If x=2, A=4>B=2 (A greater). If x=0.5, A=0.25<B=0.5 (B greater). If x=1, both equal 1. Since different cases give different results, the relationship cannot be determined.
2. Quantity A: the number of distinct prime factors of 60 Quantity B: the number of distinct prime factors of 90. Which is correct?
Explanation. 60 = 2²·3·5, so distinct primes are {2,3,5} = 3. 90 = 2·3²·5, distinct primes {2,3,5} = 3. Both equal 3.
3. It is given that x > 0. Quantity A: x + 1/x Quantity B: 2. Which is correct?
Explanation. By AM-GM, for x>0, x + 1/x ≥ 2, with equality only when x=1. So A could be equal to B (x=1) or greater (x≠1). Since equality is possible and strict inequality is also possible, no single relationship always holds — the answer is cannot be determined.
4. Quantity A: 0.2% of 500 Quantity B: 2% of 50. Which is correct?
Explanation. A = 0.002·500 = 1. B = 0.02·50 = 1. Both equal 1, so the quantities are equal.
5. Given that n is a positive integer. Quantity A: (-1)^n Quantity B: (-1)^(n+1). Which is correct?
Explanation. If n is even, A=1 and B=-1 (A greater). If n is odd, A=-1 and B=1 (B greater). They are never equal but the relationship flips depending on parity, so it cannot be determined.
6. A circle has radius r. Quantity A: the circumference Quantity B: the area. (r > 0.) Which is correct?
Explanation. Circumference = 2πr, Area = πr². Compare 2πr vs πr² → divide by πr (positive): 2 vs r. If r<2, circumference greater; if r>2, area greater; if r=2, equal. The relationship cannot be determined.
7. It is given that 3x − 7 = 11. Quantity A: x Quantity B: 5. Which is correct?
Explanation. Solve: 3x = 18, so x = 6... wait check: 3x−7=11 → 3x=18 → x=6. Comparing x=6 with 5, Quantity A would be greater. Correction: the equation gives x=6 > 5, so A is greater.
8. The average (arithmetic mean) of 5 numbers is 12. Quantity A: the sum of the 5 numbers Quantity B: 55. Which is correct?
Explanation. Sum = average × count = 12 × 5 = 60. Since 60 > 55, Quantity A is greater. The mean directly fixes the sum regardless of the individual values.
9. Given that a and b are positive and a > b. Quantity A: a/b Quantity B: (a+1)/(b+1). Which is correct?
Explanation. Compare a/b and (a+1)/(b+1). Cross-multiply (positive denominators): a(b+1) vs b(a+1) → ab+a vs ab+b → a vs b. Since a>b, a/b > (a+1)/(b+1). Quantity A is greater (adding 1 to top and bottom moves a ratio greater than 1 closer to 1).
10. A right triangle has legs of length 6 and 8. Quantity A: the length of the hypotenuse Quantity B: 9. Which is correct?
Explanation. Hypotenuse = √(6²+8²) = √(36+64) = √100 = 10. Since 10 > 9, Quantity A is greater.
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FAQ
What does 'cannot be determined' mean in quantitative comparison?
It means there is no single answer that holds in all allowed cases. If you can find one valid scenario where A>B and another valid scenario where A<B (or A=B), then the answer is choice D. This option is only available in Quantitative Comparison questions, never in standard multiple-choice.
What is the best general strategy for QC questions?
Try to simplify both quantities using the same operations (add, subtract, multiply or divide by the same positive number) to make them comparable. When variables are involved, plug in strategic test values: 0, 1, a fraction between 0 and 1, a negative number, and a large number. If different values give different relationships, the answer is 'cannot be determined.'
Are there operations I should avoid when comparing the two quantities?
Yes. You may add or subtract the same value from both quantities freely, and multiply or divide both by the same POSITIVE number. But never multiply or divide by a variable or expression that could be negative or zero, since that can reverse the inequality or be undefined.