PSAT Math Multiple-Choice Question 42: Answer and Explanation

Question: 42

Based on the system of equations above, what is the value of v?

• A. -4
• B. -3
• C. -1
• D. 0

Correct Answer: A

Explanation:

A

The question asks for the value of the variable x 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 v and starting with (B). Plug v = - 3 into one of the equations and work the steps of the question to solve for u. Plug v = -3 into the second equation because it does not contain fractions and will be quicker to solve than the first equation. The equation becomes 2(-3) = 7 + 5u, or -6 = 7 + 5u. Solve for u to get u = -. Next, plug the values for u and v into the first equation to see if the equation holds true. The equation becomes . This simplifies to , or = 3. This is not true, so eliminate (B). If it is not clear if a larger or smaller value is needed, just pick a direction to go in. Try (A) next. Plug v = - 4 into the second equation to get 2(-4) = 7 + 5u, or -8 = 7 + 5u. Solve for u to get u = -3. Next, plug the values for u and v into the first equation to see if the equation holds true. The equation becomes . This simplifies to , or = 4. This is true. Since (A) works, stop here. The correct answer is (A).