PSAT Math Multiple-Choice Question 523: Answer and Explanation

Question: 523

–9(3t – 3v) + (9t – 13v)

Which of the following expressions is equivalent to the expression above?

• A. –18t – 40v
• B. –18t + 14v
• C. 36t +14v
• D. 36t – 40v

Correct Answer: B

Explanation:

B

The question asks for an equivalent form of an expression. There are variables in the answer choices, so plug in. Make t = 1 and v = 2. The expression becomes –9[3(1) – 3(2)] + [9(1) – 13(2)] = –9(3 – 6) + (9 – 26) = –9(–3) – 17 = 27 – 17 = 10. This is the target value; circle it. Now plug t = 1 and v = 2 into the answer choices to see which one matches the target value. Choice (A) becomes –18(1) –40(2) = –18 – 80 = –98. This does not match the target value, so eliminate (A). Choice (B) becomes –18(1) + 14(2) = –18 + 28 = 10. This matches the target value, so keep (B), but check the remaining answers, just in case. Choice (C) becomes 36(1) + 14(2) = 36 + 28 = 64. Eliminate (C). Choice (D) becomes 36(1) – 40(2) = 36 – 80 = –44. Eliminate (D). The correct answer is (B).