PSAT Math Multiple-Choice Question 33: Answer and Explanation

Question: 33

Luciano measured the amount of water that evaporated over a period of time from a container holding w ounces of water, where w is greater than 12. By the end of the first day, the cup had lost 2 ounces of water. By the end of the 7th day, the cup had lost an additional 8 ounces of water. By the end of the 11th day, the cup had lost half of the water that remained after the 7th day. Which of the following represents the remaining amount of water, in ounces, in Luciano's container at the end of the 11th day?

• A.
• B. - 10
• C. w - 10
• D.

Correct Answer: D

Explanation:

D

The question asks for an expression that models a specific situation. There are variables in the answer choices, so plug in. Note that w > 12. Make w = 20. Now work the question in Bite-Sized Pieces. By the end of the first day, Luciano's cup has 20 - 2 = 18 ounces. At the end of 7 days, Luciano's cup has 18 - 8 = 10 ounces. Half of the remaining water is 5 ounces, so after 11 days, Luciano's cup would hold 10 - 5 = 5 ounces. This is the target value; circle it. Now plug w = 20 into the answer choices to see which one matches the target value. Choice (A) becomes . This does not match the target, so eliminate (A). Choice (B) becomes . Continue simplifying to get 9 - 10 = -1. Eliminate (B). Choice (C) becomes (20) - 10 = 10 - 10. This equals 0, so eliminate (C). Choice (D) becomes . This equals 5, which matches the target. The correct answer is (D).