PSAT Math Multiple-Choice Question 498: Answer and Explanation

Question: 498

Albert: t = 9h

Buster: t = 3h

The equations above show the number of trees, t, chopped per hour, h, by two lumberjacks, Albert and Buster. Based on these equations, which of the following statements is true?

• A. The rate at which Buster chopped trees per hour decreased at a slower rate than the rate at which Albert chopped trees per hour.
• B. The rate at which Albert chopped trees per hour decreased at a slower rate than the rate at which Buster chopped trees per hour.
• C. For every hour of chopping, the number of trees Albert chopped was one-third as many as the number of trees Buster chopped.
• D. For every hour of chopping, the number of trees Buster chopped was one-third as many as the number of trees Albert chopped.

Correct Answer: D

Explanation:

D

The question asks for a true statement about two equations. The equations compare the number of trees chopped, t, to the number of hours, h, for two lumberjacks. Plug and play to determine the relationship between the two equations. Make h = 1. In that case, Albert chops 9(1) = 9 trees and Buster chops 3(1) = 3 trees. In the same amount of time, Albert chops three times as many trees as Buster. Eliminate answer choices that do not match this information. Choice (A) states that the rate at which Buster chops trees per hour decreases at a slow rate than Albert's, and (B) states that the rate at which Albert chops tress per hour decreases at a slow rate than Buster's. Not enough is known at this point to see how the rate will change over time, so keep (A) and (B) for now. Choice (C) states that for every hour of chopping, Albert chopped one-third as many trees as Buster. Albert chopped more trees than Buster in one hour, so eliminate (C). Choice (D) states that for every hour of chopping, Buster chopped one-third as many trees as Albert. This is true and likely the correct answer, but to double-check (A) and (B), plug in h = 2 to determine what happens to the rate for each lumberjack. If h = 2, Albert chops 9(2) = 18 trees, which is the same as 9 trees/hour. In 2 hours, Buster would chop 3(2) = 6 trees, which is the same as 3 trees/hour. Each lumberjack's rate is the same as when h = 1, which means there is no decrease in either Albert's or Buster's rate. Eliminate (A) and (B). The correct answer is (D).