PSAT Math Multiple-Choice Question 71: Answer and Explanation

Question: 71

Delphine is studying the growth of bacteria in a petri dish. She grows 100 colonies of bacteria in dishes at varying temperatures to find the optimal temperature for bacteria growth. The temperature of the 10 colonies with the most rapid growth is used to determine the optimal temperature range, which Delphine finds to be from 30° to 37°C, inclusive. Which of the following inequalities represents the optimal temperature range, t, for bacteria growth?

• A. |t + 7|≤ 37
• B. |t - 3.5| ≤ 33.5
• C. |t - 30|≤ 7
• D. |t - 33.5| ≤ 3.5

Correct Answer: D

Explanation:

D

The question asks for an inequality that represents a given situation. There are variables in the answer choices, so plug in. Plug in a value for t from the optimal temperature range (30–37) and use Process of Elimination. If t = 37, the correct answer will provide a statement that is true. Plug t = 37 into the answers and eliminate any answers that are not true. Choice (A) becomes |37 + 7| ≤ 37 or |44| ≤ 37. Since this statement is false, eliminate (A). Choice (B) becomes |37 - 3.5| ≤ 33.5 or |33.5| ≤ 33.5. Since this statement is true, keep (B). Choice (C) becomes |37 - 30| ≤ 7, or |7| ≤ 7. Since this statement is true, keep (C). Choice (D) becomes |37 - 33.5| ≤ 3.5, or |3.5| ≤ 3.5. Since this statement is true, keep (D). Next, plug in a value that is not in the optimal temperature range, such as t = 29, and eliminate any answers that provide a true statement. Choice (B) becomes |29 - 3.5| ≤ 33.5 or |25.5| ≤ 33.5. Since this statement is true, eliminate (B). Choice (C) becomes |29 - 30| ≤ 7 or |-1| ≤ 7. Since this statement is true eliminate (C). The correct answer is (D).