Multiple choice

Directions: Choose the most appropriate option for the following question. How many times from 4 pm to 10 pm are the hands of a clock at right angles?

  1. 9

  2. 10

  3. 11

  4. 6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The hands of a clock are at right angles twice every hour, except for the periods 2-4 pm and 8-10 pm, where they only occur 3 times instead of 4. From 4 pm to 10 pm (6 hours), there are 11 right-angle positions.

AI explanation

The hands of a clock form a right angle every 32 8/11 minutes, which means the formula for right angles is |30(H) - 5.5(M)| = 90 or 270. Between 4:00 and 5:00, the hands are perpendicular at 240/11 minutes and 600/11 minutes, occurring exactly twice. Checking the remaining hours from 5:00 to 10:00 reveals the hands turn perpendicular exactly twice during each of these hours as well. Adding the 2 occurrences from the first hour to the 9 occurrences from the remaining hours yields a total of 11 times.

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