GRE Quantitative Comparison Strategies 2 โ Questions and Answers
Question 1: Quantity A: x. Quantity B: x^2. Given no restriction on x, which is correct?
- Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined (Correct answer)
Correct answer: The relationship cannot be determined
For 0<x<1, x>x^2; for x>1, x^2>x; at x=0 or 1 they are equal, so the relationship varies.
Question 2: Quantity A: the average of 10 and 20. Quantity B: the average of 12 and 18. Which is correct?
- Quantity A is greater
- Quantity B is greater
- The two quantities are equal (Correct answer)
- The relationship cannot be determined
Correct answer: The two quantities are equal
Both pairs sum to 30, so each average equals 15.
Question 3: Given x < 0, Quantity A: x^3. Quantity B: x^2. Which is correct?
- Quantity A is greater
- Quantity B is greater (Correct answer)
- The two quantities are equal
- The relationship cannot be determined
Correct answer: Quantity B is greater
A negative number cubed is negative while its square is positive, so x^2 is greater.
Question 4: Quantity A: 25% of 80. Quantity B: 80% of 25. Which is correct?
- Quantity A is greater
- Quantity B is greater
- The two quantities are equal (Correct answer)
- The relationship cannot be determined
Correct answer: The two quantities are equal
Percent expressions are commutative: 25% of 80 = 80% of 25 = 20.
Question 5: A circle has radius r. Quantity A: its circumference. Quantity B: its area, given r = 2. Which is correct?
- Quantity A is greater
- Quantity B is greater
- The two quantities are equal (Correct answer)
- The relationship cannot be determined
Correct answer: The two quantities are equal
At r=2, circumference is 4ฯ and area is 4ฯ, so they are equal.
Question 6: Given that n is a positive integer, Quantity A: 2^n. Quantity B: n^2. Which is correct?
- Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined (Correct answer)
Correct answer: The relationship cannot be determined
At n=2 they are equal, at n=3 they are equal, but at n=2 vs others the order changes (e.g., n=2 equal, n=3 equal, n=1 A greater), so it varies.
Question 7: Quantity A: the number of distinct prime factors of 12. Quantity B: the number of distinct prime factors of 30. Which is correct?
- Quantity A is greater
- Quantity B is greater (Correct answer)
- The two quantities are equal
- The relationship cannot be determined
Correct answer: Quantity B is greater
12 = 2^2ยท3 has two prime factors while 30 = 2ยท3ยท5 has three, so Quantity B is greater.
GRE Quantitative Comparison Strategies 2
Quantity A: x.
Quantity B: x^2.
Given no restriction on x, which is correct?