GRE Quantitative Comparison Strategies 3 — Questions and Answers
Question 1: Given 0 < a < b, Quantity A: 1/a. Quantity B: 1/b. Which is correct?
- Quantity A is greater (Correct answer)
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined
Correct answer: Quantity A is greater
For positive numbers, the larger denominator gives the smaller reciprocal, so 1/a > 1/b.
Question 2: Quantity A: the perimeter of a square with area 16. Quantity B: the perimeter of a rectangle 2 by 8. 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
The square has side 4 and perimeter 16, while the rectangle has perimeter 2(2+8)=20.
Question 3: Given x + y = 10, Quantity A: xy. Quantity B: 25. 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
With a fixed sum of 10, xy is maximized at x=y=5 giving 25, so xy is at most 25.
Question 4: Quantity A: 3/7. Quantity B: 4/9. 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
Cross-multiplying gives 3·9=27 versus 4·7=28, so 4/9 is greater.
Question 5: Given x is an integer with -3 ≤ x ≤ 3, Quantity A: |x|. Quantity B: 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
|x| ranges from 0 to 3 across the allowed values, so it can be less than, equal to, or greater than 2.
Question 6: Quantity A: the median of {2, 4, 6, 8, 100}. Quantity B: the mean of {2, 4, 6, 8, 100}. 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
The median is 6 while the mean is 120/5=24, so the mean is greater because of the outlier.
Question 7: Given a triangle has two sides of length 5 and 9, Quantity A: the third side's length. Quantity B: 14. 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
By the triangle inequality the third side must be less than 5+9=14, so Quantity B is greater.
GRE Quantitative Comparison Strategies 3
Given 0 < a < b, Quantity A: 1/a.
Quantity B: 1/b.
Which is correct?