PSAT Math Multiple-Choice Question 17: Answer and Explanation

Question: 17

Which of the following is a true statement about the equation above?

• A. There are no solutions to the equation.
• B. The solution is p = 2.
• C. The solution is p = 3.
• D. There are infinitely many solutions to the equation.

Correct Answer: A

Explanation:

A

The question asks for a true statement about the equation. Solve the equation to find the true statement. Since the denominator of both equations is p - 2, set both numerators equal to each other to get 2(p - 2) + 2(3 - p) = 2(3p - 6) + 3(6 - 2p). Distribute the numbers in front of the parentheses to get 2p - 4 + 6 - 2p = 6p - 12 + 18 - 6p. Combine like terms to get 2 = 6. Since this statement is false and the variables were eliminated, the equation has no solutions. The correct answer is (A).