GRE Quantitative Comparison Strategies 2

Question 1

Quantity A: x. Quantity B: x^2. Given no restriction on x, which is correct?

Accepted Answer

The relationship cannot be determined

Answer

For 0x^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?

Accepted Answer

The two quantities are equal

Answer

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?

Accepted Answer

Quantity B is greater

Answer

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?

Accepted Answer

The two quantities are equal

Answer

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?

Accepted Answer

The two quantities are equal

Answer

At r=2, circumference is 4π and area is 4π, so they are equal.

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