Multiple choice

At noon and at midnight the long and short hands of a clock are together. Between noon and midnight, how many times the long hand overtakes the short hand?

  1. $9$
  2. $10$
  3. $11$
  4. $12$
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C Correct answer
Explanation

The hands of a clock overlap every 65 and 5/11 minutes. In a 12-hour period, they overlap 11 times. Since the interval is from noon to midnight (12 hours), the hands overlap 11 times.

AI explanation

The hands of a clock start together at exactly noon. Using the concept of relative speed, the minute hand completes a full lap over the hour hand every 12/11 hours. Over the 12-hour period from noon to midnight, this overtaking occurs exactly 11 times before they align again at midnight. Therefore, the long hand overtakes the short hand 11 times.

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