GRE Quantitative Comparison Strategies 3

Question 1

Given 0 < a < b, Quantity A: 1/a. Quantity B: 1/b. Which is correct?

Accepted Answer

Quantity A is greater

Answer

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?

Accepted Answer

Quantity B is greater

Answer

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?

Accepted Answer

Quantity B is greater

Answer

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?

Accepted Answer

Quantity B is greater

Answer

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?

Accepted Answer

The relationship cannot be determined

Answer

|x| ranges from 0 to 3 across the allowed values, so it can be less than, equal to, or greater than 2.

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