PSAT Math Multiple-Choice Question 103: Answer and Explanation

Question: 103

Which of the following is an equivalent form of the expression 30y - 12cy?

• A. (5 - 2c)y
• B. (30 - 12c)y
• C. 18(c - 2y)
• D. 18cy²

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 y = 2 and c = 3. The expression becomes 30(2) - 12(3)(2) = 60 - 72 = -12. This is the target value; circle it. Now plug y = 2 and c = 3 into the answer choices to see which one matches the target value. Choice (A) becomes [5 - 2(3)](2) = (5 - 6)(2) = (-1)(2) = -2. This does not match the target, so eliminate (A). Choice (B) becomes [30 - 12(3)](2) = (30 - 36)(2) = (-6)(2) = -12. Keep (B), but check (C) and (D) just in case. Choice (C) becomes (18)[3 - 2(2)] = (18)(3 - 4) = (18)(-1) = -18. Eliminate (C). Choice (D) becomes (18)(3)(2)² = (18)(3)(4), which does not equal -12. Eliminate (D). The correct answer is (B).