Quantitative Comparison Strategies Flashcards

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

Answer: The relationship cannot be determined

For 0x^2; for x>1, x^2>x; at x=0 or 1 they are equal, so the relationship varies.

Quantity A: the average of 10 and 20. Quantity B: the average of 12 and 18. Which is correct?

Answer: The two quantities are equal

Both pairs sum to 30, so each average equals 15.

Given x < 0, Quantity A: x^3. Quantity B: x^2. Which is correct?

Answer: Quantity B is greater

A negative number cubed is negative while its square is positive, so x^2 is greater.

Quantity A: 25% of 80. Quantity B: 80% of 25. Which is correct?

Answer: The two quantities are equal

Percent expressions are commutative: 25% of 80 = 80% of 25 = 20.

A circle has radius r. Quantity A: its circumference. Quantity B: its area, given r = 2. Which is correct?

Answer: The two quantities are equal

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

Given that n is a positive integer, Quantity A: 2^n. Quantity B: n^2. Which is 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.

Quantity A: the number of distinct prime factors of 12. Quantity B: the number of distinct prime factors of 30. Which is correct?

Answer: Quantity B is greater

12 = 2^2·3 has two prime factors while 30 = 2·3·5 has three, so Quantity B is greater.