Multiple choice

How many times are the two hands of a clock perpendicular to each other in every 12 hours?

  1. 24

  2. 22

  3. 44

  4. 11

  5. 12
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B Correct answer
Explanation

The hands of a clock are perpendicular twice every hour, except during the intervals around 3:00 and 9:00 where they are perpendicular only once. Thus, in 12 hours, they are perpendicular 22 times.

AI explanation

In one hour, the minute hand completes a full 360 degree circle while the hour hand moves 30 degrees, causing them to overlap once and form a perpendicular angle twice. Over a 12 hour period, this would mathematically result in 24 perpendicular positions, but a right angle is technically never formed exactly at the overlaps. The hands are perpendicular at 22 distinct times, since both the 3:00 and 9:00 marks are skipped as the initial states, making the total 22.

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