Problem 3 · 2012 Math Kangaroo
Easy
Geometry & Measurement
transformations
A wristwatch was laid on a table in such a way that the minute hand pointed northeast. How many minutes must pass before the minute hand is pointing northwest for the first time?
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Answer: A — 45
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Hint 1 of 2
The minute hand turns clockwise; mark NE and NW on a compass.
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Hint 2 of 2
Going clockwise from NE all the way round to NW is three quarters of a turn.
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Approach: turn the compass directions into a fraction of a full hour
- Northeast and northwest are 90° apart, but the minute hand turns clockwise, so it must swing the long way: NE → SE → SW → NW.
- That is 270°, which is three quarters of a full 360° turn.
- A full turn of the minute hand takes 60 minutes, so three quarters takes 45 minutes.
- The answer is 45 (A).
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