PSAT Math Multiple-Choice Question 52: Answer and Explanation

Question: 52

Monster Truck Inc. leases a new truck for a down payment of $3,200 plus monthly payments of $380 per month for 36 months. Which of the following functions, f, represents the total amount paid, in dollars, after m months, where 0 ≤ m ≤ 36?

• A. f(m) = 380 + 3,200m
• B. f(m) = 3,200 + 36m
• C. f(m) = 3,200 + 380m
• D. f(m) = 10,480 - 380m

Correct Answer: C

Explanation:

C

The question asks for the equation of a function. Notice that there are variables in the question and in the answer choices, so try to plug in. Since m represents months, plug in a number that works easily with the question. The number must be within the range 0 ≤ m ≤ 36, so choose m = 10. After 10 months, the total amount paid will be: $3,200 (the down payment) + $380 × 10 months, or 3,200 + (380)(10) = $7,000. This is the target value; circle it. Now plug m = 10 into each answer choice to see which one matches the target value. Choice (A) becomes f(10) = 380 + 3,200(10). 3,200(10) is much larger than the target value, so eliminate (A). Choice (B) becomes f(10) = 3,200 + 36(10), or 3,560. This does not match the target value, so eliminate (B). Choice (C) becomes f(10) = 3,200 + 380(10). This matches the target value, so keep (C), but check (D) just in case. Choice (D) becomes f(10) = 10,480 - 380(10), or 6,680. This does not match the target value, so eliminate (D). The correct answer is (C).