PSAT Math Multiple-Choice Question 551: Answer and Explanation

Question: 551

The United States primarily uses a 12-hour clock with 12-hour periods for the morning (a.m.) and for the afternoon/evening (P.M.). Much of the rest of the world uses a 24-hour clock. Which of the following inequalities expresses the digits for hours, H, on a 24-hour clock that correspond to the business hours for a restaurant that is open from 7 P.M. until 11 P.M.

• A. 7 ≤ H ≤ 11
• B. 12 ≤ H ≤ 24
• C. 19 ≤ H ≤ 23
• D. 24 ≤ H ≤ 27

Correct Answer: C

Explanation:

(C) Simply add 12 to both 7 and 11 to find the correct range since all of the P.M. times are 12 hours less than the time on a 24-hour clock:

12 + 7 = 19 and 12 + 11 = 23

This makes the range between 19 and 23 hours inclusive, which is expressed as the inequality 19 ≤ H ≤ 23.