PSAT Math Multiple-Choice Question 97: Answer and Explanation

Question: 97

For all y > 3, which of the following is equivalent to the expression above?

• A. 3 - y
• B.
• C.
• D. 2y² + 6y

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. Since y must be greater than 3, make y = 4. The expression becomes , which is . To subtract fractions, make the denominators the same. One common denominator of 7 and 8 is 56. Multiply the numerator and denominator of by 7 to get . Multiply the numerator and denominator of by 8 to get . The expression becomes , which is . To divide by a fraction, multiply the numerator by the reciprocal of the denominator to get 1 × or -56. This is the target value; circle it. Now plug y = 4 into the answer choices to see which one matches the target value. Choice (A) becomes 3 - 4 or -1. This does not match the target, so eliminate (A). Choice (B) becomes , which is . Multiplying gives , which is -56. Keep (B) but check the remaining answer choices just in case. Choice (C) is the reciprocal of (B), so it will equal . Eliminate (C). Choice (D) is the numerator of (B), so it will equal 56. Eliminate (D). The correct answer is (B).