PSAT Math Multiple-Choice Question 306: Answer and Explanation

Question: 306

If 36 + 3(4x - 9) = c(2x + 1) + 25 has no solution and c is a constant, what is the value of c ?

• A. -3
• B. 3
• C. 6
• D. 12

Correct Answer: C

Explanation:

C

Difficulty: Medium

Getting to the Answer: If a linear equation has no solution, the variables cancel out, leaving two numbers that are not equal to each other. Start by simplifying the left side of the equation:

The variable term on the left is 12x. Because the variable terms must cancel, the right side of the equation must also have a 12x, so it must be that c = 6, which is (C).