How to find the angle of clock hands - GRE Quantitative Reasoning

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Question

What is the angle between the hour and minute hand of a clock at 4:15?

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Answer

In this case, the minute hand is pointing at 3 while the hour hand is pointing at some value past 4. Now, since 15 minutes represents 1/4 of an hour, the hour hand will be 1/4 the distance between 4 and 5. The total number of degrees between minutes is 360/12 = 30°; therefore, the hour hand is 30/4 or 7.5° past the 4 o'clock point. Now, between 3 and 4, there are 30°. Add to that the 7.5°. The total distance is therefore 37.5°.

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