PSAT Math Multiple-Choice Question 60: Answer and Explanation

Question: 60

Aubri determines that her score in a particular video game can be calculated using the formula x⁴ - y⁴, where x represents the number of treasures she discovers, and y represents the number of hidden traps she falls into. Which of the following expressions would be a suitable equivalent for Aubri's score calculation formula?

• A. (x + y) (x - y) (x² + y²)
• B. (x + y)²(x² + y²)
• C. (x - y)²(x² + y²)
• D. (x + y)(x - y)(x² - y²)

Correct Answer: A

Explanation:

A

The question asks for an equivalent form of an expression. There are variables in the answer choices, so plug in. Make x = 3 and y = 2. The expression becomes 3⁴ - 2⁴ = 81 - 16 = 65. This is the target value; circle it. Now plug x = 3 and y = 2 into the answer choices to see which one matches the target value. Choice (A) becomes (3 + 2)(3 - 2)(3² + 2²) = (5)(1)(9 + 4) = (5)(1)(13) = 65. This matches the target value, so keep (A), but check the remaining answers just in case. Choice (B) becomes (3 + 2)²(3² + 2²) = (5²)(9 + 4) = (25)(13) = 325. Eliminate (B). Choice (C) becomes (3 - 2)²(3² + 2²) = (1)²(9 + 4) = (1)(13) = 13. Eliminate (C). Choice (D) becomes (3 + 2)(3 - 2)(3² - 2²) = (5)(1)(9 - 4) = (5)(1)(5) = 25. Eliminate (D). The correct answer is (A).