Question

How many times between 4 am and 4 pm will the hands of a clock cross?

• A. 4
• B. 8
• C. 10
• D. 11

Answer 1

Answer:

D. 11

The Shortcut

• Clock hands cross 11 times every 12 hours.

• Clock hands cross 22 times every 24 hours.

Since 4 AM to 4 PM is exactly a 12-hour window, the answer is simply 11 times.

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Why 11 instead of 12?

The hands only cross once during the 2-hour block between 11:00 and 1:00, right at 12:00. This "loses" one crossover event, dropping the total from 12 down to 11.

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Quick Formula for Exact Timing

To find exactly when they cross between any hour $H$ and the next hour:
$\text{Minutes} = \frac{60}{11} \times H$

• Example for 4 o'clock ($H=4$):
  $\frac{60}{11} \times 4 = \frac{240}{11} = \mathbf{21\frac{9}{11}\text{ minutes}}$ (approx. 4:21).