Multiple choice

At what time between 3 and 4 o'clock will the hands of the clock be exactly at right angles (i.e., 90 degrees apart) for the first time?

  1. 3:21 (9/11)

  2. 3:16 (4/11)

  3. 3:32 (8/11)

  4. 3:22 (7/11)

  5. 3:12 (7/11)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

At 3 o'clock, the hands are 90 degrees apart. For the first time after 3, the minute hand must gain distance. The formula for the angle between hands is |30H - 5.5M|. For 90 degrees, |30(3) - 5.5M| = 90. 90 - 5.5M = -90 (not possible) or 5.5M - 90 = 90. 5.5M = 180, M = 180 / 5.5 = 360/11 = 32 8/11.

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