PSAT Math Multiple-Choice Question 502: Answer and Explanation

Question: 502

What is the value of z given the equation 4(z + 3) – 6 = 5(z – 1)?

• A. 11
• B. 7
• C. 2
• D. –2

Correct Answer: A

Explanation:

A

The question asks for the solution to the equation. Since the question asks for a specific value and the answers contain numbers in decreasing order, plug in the answers and look for the answer choice that makes the equation true. Begin by labeling the answers as "z" and start with (B), 7. Plug (B) into the equation to get 4(7 + 3) – 6 = 5(7 – 1). Simplify both sides to get 4(10) – 6 = 5(6) and then 34 = 30. Since this is not true, eliminate (B). Even though both sides are not equal, they are close, so choose an answer choice close in value to (B), 7. Since (A), 11 is closer in value to (B), 7, than (C) –2, plug (A) into the equation next. The equation becomes get 4(11 + 3) – 6 = 5(11 – 1). This simplifies to 4(14) – 6 = 5(10) and then 50 = 50, which is true. The correct answer is (A).