Problem 5 · 1986 AJHSME
Easy
Number Theory
time-arithmetic
A contest began at noon one day and ended 1000 minutes later. At what time did the contest end?
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Answer: D — 4:40 a.m.
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Hint 1 of 2
1000 loose minutes is hard to add to a clock. What unit would make adding to "noon" easy?
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Hint 2 of 2
Trade the minutes in for hours: how many whole hours fit in 1000 minutes, and how many minutes are left over?
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Approach: convert minutes to hours-and-minutes, then add
- Clocks count in hours, so first turn 1000 minutes into hours. Since 60 minutes make an hour, 1000 ÷ 60 = 16 with 40 left over: that's 16 hours 40 minutes.
- Add to noon. 16 hours past noon: noon + 12 h = midnight, then + 4 more h = 4:00 a.m.; the leftover 40 minutes makes 4:40 a.m. the next day.
- Why split off the 12 first: jumping straight to midnight handles the a.m./p.m. flip cleanly, so you don't accidentally land on 4:40 p.m.
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