Problem 5 · 2011 AMC 8
Easy
Arithmetic & Operations
time-conversion
What time was it 2011 minutes after midnight on January 1, 2011?
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Answer: D — January 2 at 9:31 AM.
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Hint 1 of 2
2011 minutes is more than one day — a full day is only 24×60 = 1440 minutes. Peel off one whole day first, and the leftover tells you the clock time.
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Hint 2 of 2
Convert minutes to hours-and-minutes by dividing by 60: the quotient is hours, the remainder is the minutes.
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Approach: peel off a full day, then convert the leftover
- One day = 1440 minutes. 2011 − 1440 = 571 minutes into the next day, January 2.
- 571 ÷ 60 = 9 remainder 31, so that's 9 hours 31 minutes after midnight = 9:31 AM on January 2.
- Worth keeping: clock and calendar questions are all about remainders — throw away whole days (1440 min) or whole 12-hour blocks, and only the remainder decides the answer.
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