Multiple choice

How many times between 4 a.m. and 5 a.m. the minute and hour hands of a clock will be at right angles?

  1. $2$
  2. $3$
  3. $4$
  4. $1$
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A Correct answer
Explanation

The hands are at right angles twice every hour, except during the 3 o'clock and 9 o'clock hours. Between 4 and 5, they are at right angles at approximately 4:05 and 4:38.

AI explanation

At 4:00 am the hands form a 120 degree angle, so the minute hand must move 30 degrees to reach the first 90 degree right angle at about 4:05. The minute hand then passes the hour hand and must create a second 90 degree angle before 5:00 am at about 4:38. Therefore, the hands are at right angles exactly 2 times in this hour.

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