Multiple choice

How many times between 3:30 and 4:15 will the hands of a clock be at right angles?

  1. 0

  2. 1

  3. 2

  4. 3

  5. 4
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C Correct answer
AI explanation

At 3:30, the minute hand is at 6 and the hour hand is halfway between 3 and 4, placing them 75 degrees apart. By 4:15, the minute hand is at 3 and the hour hand is slightly past 4, making them 7.5 degrees apart. Since the separation continuously decreases from 75 degrees to 7.5 degrees during this period, it must pass through exactly 90 degrees and 270 degrees once each, meaning the hands are at right angles twice.

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