PSAT Math Multiple-Choice Question 150: Answer and Explanation

Question: 150

Which of the following describes the solution to the equation shown above?

• A. The only solution is y = 1.
• B. The only solution is y = 10.
• C. The equation has infinitely many solutions.
• D. The equation has no solutions.

Correct Answer: C

Explanation:

C

The question asks about the solutions to the equation. Two of the choices include numbers, and the other two are infinitely many solutions and no solutions. Plug in the easier of the choices with numbers. Plug in y = 10 to get . The equation becomes 5(5 + 5) = 20 + 5 + 25 or 5(10) = 50. Since this is true, y = 10 is a solution. Eliminate (A), since y = 1 cannot be the only solution, and eliminate (D), since there is at least one solution. It is still possible that there are infinitely many solutions. To test, plug in any other number. To make the math as easy as possible, plug in y = 0 to get . The equation becomes 5(0 + 5) = 0 + 0 + 25 or 5(5) = 25. Therefore, y = 0 is also a solution. Since y = 10 is not the only solution, eliminate (B). The correct answer is (C).