PSAT Math Multiple-Choice Question 140: Answer and Explanation

Question: 140

(3 - y)² - (3 - y)

Which of the following is an equivalent form of the expression above?

• A. 3 - y
• B. y² - 7y + 6
• C. (3 - y)(2 - y)
• D. 9 - y²

Correct Answer: C

Explanation:

C

The question asks for an equivalent form of an expression. There are variables in the answer choices, so plug in. Make y = 2. The expression becomes (3 - 2)² - (3 - 2), which is (1)² - 1 or 0. This is the target value; circle it. Now plug y = 2 into the answer choices to see which one matches the target value. Choice (A) becomes 3 - 2 or 1. This does not match the target, so eliminate (A). Choice (B) becomes 2² - 7(2) + 6, which is 4 - 14 + 6 or -4; eliminate (B). Choice (C) becomes (3 - 2)(2 - 2), which is (1)(0) or 0; keep (C), but check (D) just in case. Choice (D) becomes 9 - 2², which is 9 - 4 or 5; eliminate (D). The correct answer is (C).