PSAT Math Multiple-Choice Question 623: Answer and Explanation

Question: 623

In basketball, 1 point is awarded for a free throw, 2 points for a shot within the three-point line, and 3 points for shots outside the three-point line. If the number of points from x two-point shots is at least as great as the number of points from y three-point shots and z free throws, which expression would represent this relationship?

• A. x ≥ y + z
• B. x ≥ 3y + z
• C. 2x ≥ 3y + z
• D. 2x ≥ y + 3z

Correct Answer: C

Explanation:

(C) The number of points from x two-point shots will be 2x. Similarly, making y three-point shots and z free throws corresponds to 3y points and z points, respectively. So the number of points earned from y three-point shots combined with z free throws will be 3y + z. If the number of points from the two-point shots has to be at least as much (implying at least as much if not more) than the combined points from three-pointers and free throws, it follows that:

2x ≥ 3y + z

This is choice (C).

Choice (A) doesn't work because it doesn't take into account the different values of each shot.

Choice (B) doesn't account for each two-point shot giving 2 points.

Choice (D) implies that three-point shots score only 1 point and that free throws score points.