Problem 7 · 2011 Math Kangaroo
Easy
Arithmetic & Operations
careful-counting
The bell of a clocktower rings every full hour (8:00, 9:00, 10:00 etc.) and rings as many times as the number of hours. It also rings once on every half hour (8:30, 9:30, 10:30 etc.). How often will it ring between 7:55 and 10:45?
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Answer: D — 30 times
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Hint 1 of 2
List every full hour and every half hour strictly between 7:55 and 10:45.
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Hint 2 of 2
A full hour rings as many times as the hour number; each half hour rings once.
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Approach: count rings by occasion
- Full hours in the window: 8:00 rings 8, 9:00 rings 9, 10:00 rings 10, total 27 rings.
- Half hours 8:30, 9:30, 10:30 each ring once, adding 3.
- Total = 27 + 3 = 30 times, answer D.
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