Multiple choice

At what time between 2 PM and 3 PM will the hour and minute hands of a clock be exactly opposite each other?

  1. 2:16:21

  2. 2:27:16

  3. 2:43:38

  4. 2:49:45
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C Correct answer
Explanation

At 2 PM, the minute hand is at 12 and the hour hand is at 2. For the hands to be opposite, the minute hand must be 30 minutes ahead of the hour hand, meaning it must be at the 8 o'clock position (40 minutes). Using the formula M = (2/11) * (30 * H + 30), where H=2, we get M = (2/11) * 90 = 180/11 = 16.36 minutes, which corresponds to 2:43:38 when calculating the exact position for the hands to be 180 degrees apart.

AI explanation

Using the formula for overlapping hands, we calculate when the hands form an angle of 180 degrees. At 2 PM, the initial angle is 60 degrees, so the minute hand needs to cover an additional 180 degrees, making the target gap 240 degrees. Plugging this into the formula gives time as 240 divided by 5.5, which equals 43.636 minutes, meaning the time is 2:43:38.

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