PSAT Math Multiple-Choice Question 539: Answer and Explanation

Question: 539

The equations below show the total number of cars, t, that have passed through two intersections after d hours of daylight.

Intersection X: t = 450d

Intersection Y: t = 150d

Which of the following statements is an accurate comparison based on the equations?

• A. The number of cars that passed through Intersection X per hour increased at a faster rate than the number of cars that passed through Intersection Y per hour.
• B. For each hour of daylight, the number of cars that passed through Intersection X is three times the number that passed through Intersection Y.
• C. The number of cars that passed through Intersection Y per hour increased at a faster rate than the number of cars that passed through Intersection X per hour.
• D. For each hour of daylight, the number of cars that passed through Intersection Y is three times the number that passed through Intersection X.

Correct Answer: B

Explanation:

B

The question asks for an accurate comparison based on a system of equations. Start by reading the full question, which gives equations for the number of cars passing through two intersections. Then label the parts of the equations with the information given. The question states that t is the total number of cars passing through the intersection and d is hours of daylight. Next, use Process of Elimination to get rid of answer choices that are not consistent with the labels. Choice (A) refers to the number of cars per hour increasing at a certain rate. To check this, plug in some numbers for d. Plug in d = 1, d = 2, and d = 3 to see what happens over time.

d = 1	d = 2	d = 3
For Intersection X: t = 450(1) = 450	450(2) = 900	450(3) = 1,350
For Intersection Y: t = 150(1) = 150	150(2) = 300	150(3) = 450

Each hour, the number of cars passing through Intersection X increases by 450, and the number of cars passing through Intersection Y increases by 150. Therefore, for either intersection, the rate is constant and not increasing at all for either intersection. Eliminate (A) and (C), since both refer to an increasing rate. Compare the remaining answers. The only difference is whether the number of cars passing through Intersection X or Intersection Y is greater. Choice (D) says that the number of cars passing through Intersection Y is greater, which is not true. Intersection X has greater numbers at all values of d, so eliminate (D). The correct answer is (B).