PSAT Math Multiple-Choice Question 107: Answer and Explanation

Question: 107

Which of the following is a solution to the equation 3b² - 6b = 5 + 4b²?

• A. -5
• B. 0
• C. 1
• D. 3

Correct Answer: A

Explanation:

A

The question asks for a solution to the given equation. Since the question asks for a specific value and the answers contain numbers in increasing order, use PITA. Begin by labeling the answers as b and start with (B), 0. The equation becomes (3)(0)² - (6)(0) = 5 + (4)(0)² or 0 - 0 = 5 + 0. This isn't true, so eliminate (B). It may be difficult to see whether a larger or smaller number is needed to make the equation true, so just pick either direction. For (A), plug in b = -5 to get (3)(-5)² - (6)(-5) = 5 + (4)(-5)². Simplify this to get (3)(25) + 30 = 5 + (4)(25) or 75 + 30 = 5 + 100. This results in 105 = 105, which is true, so stop here. The correct answer is (A).