PSAT Math Multiple-Choice Question 38: Answer and Explanation

Question: 38

2(n + 5) = 3(n - 2) + 8

In the equation above, what is the value of n?

• A. 1
• B. 3
• C. 4
• D. 8

Correct Answer: D

Explanation:

D

The question asks for the value of the variable n in the given equation. Since the question asks for a specific value and the answers contain numbers in increasing order, plug in the answers. Begin by labeling the answers as n and starting with (B), 3. Plug n = 3 into the equation and work the steps of the question. The equation becomes 2(3 + 5) = 3(3 - 2) + 8, or 2(8) = 3(1) + 8. This simplifies to 16 = 11, which is false. Eliminate (B). Next, try (C). Plug n = 4 into the equation to get 2(4 + 5) = 3(4 - 2) + 8, or 2(9) = 3(2) + 8. This simplifies to 18 = 14, which is false. Eliminate (C). Next, try (D). Plug n = 8 into the equation to get 2(8 + 5) = 3(8 - 2) + 8, or 2(13) = 3(6) + 8. This simplifies to 26 = 26, which is true. Since (D) works, stop here. The correct answer is (D).