PSAT Math Multiple-Choice Question 32: Answer and Explanation

Question: 32

If and c ≠ 0, what is the value of ?

• A. ac²
• B. a²c⁴
• C.
• D.

Correct Answer: D

Explanation:

D

The question asks for the value of an expression. There are variables in the answer choices, so plug in. Pick numbers for a, b, and c such that ; , so make a = 1, b = 4, and c = 2. Now, . This is the target value; circle it. Now plug a = 1 and c = 2 into the answer choices to see which one matches the target value. Choice (A) becomes (1)(2)² = (1)(4). This becomes 4, which does not match the target, so eliminate (A). Choice (B) becomes (1)²(2)⁴ = (1)(16). This becomes 16, so eliminate (B). Choice (C) becomes . This becomes , so eliminate (C). Choice (D) becomes . This becomes , which matches the target. The correct answer is (D).