PSAT Math Multiple-Choice Question 35: Answer and Explanation

Question: 35

A certain standardized test has 50 questions. A student receives 1 point for each correct answer and loses of a point for each incorrect answer. Which of the following equations best models the net score, S, in points, for a student who completes all 50 questions and answers c of the questions correctly?

• A. S = 50 - 0.25c
• B. S = 50 - 0.75c
• C. S = c - 0.25(50 - c)
• D. S = c - 0.75(50 - c)

Correct Answer: C

Explanation:

C

The question asks for an equation that models a specific situation. There are variables in the answer choices, so plug in. The variable c appears on the more complicated side of the equations in the answers, so plug in a value for c, which is the number of correct answers. The total number of questions is 50, so c must be less than 50. Make c = 46. Now work the question in Bite-Sized Pieces. The student got 46 questions correct and 4 questions wrong. The student earned 1 point for each of the 46 correct answers and lost point for each of the 4 incorrect answers. The student's score would be (1)(46) - (4) = 46 - 1. Subtract 46 - 1 = 45. This is the target answer; circle it. Now plug c = 46 into the answer choices to see which one matches the target value. Choice (A) becomes S = 50 - 0.25(46) = 50 - 11.5. This becomes 38.5, which does not match the target, so eliminate (A). Choice (B) becomes S = 50 - 0.75(46) = 50 - 34.5. This becomes 15.5, so eliminate (B). Choice (C) becomes S = 46 - 0.25(50 - 46) = 46 - 0.25(4). Continue simplifying to get 46 - 1 = 45. This matches the target. Keep (C), but check (D) just in case. Choice (D) becomes S =46 - 0.75(50 - 46) = 46 - 0.75(4). Continue simplifying to get 46 - 3 = 43. Eliminate (D). The correct answer is (C).