2011 AMC 8 Problem 5

Attempt Problem 5 of the 2011 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2011 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

5.

What time was it 20112011 minutes after the beginning of January 1,1, 2011?2011?
January 11 at 9:319:31 PM
January 11 at 11:5111:51 PM
January 22 at 3:113:11 AM
January 22 at 9:319:31 AM
January 22 at 6:016:01 PM
Answer: D
Concepts:date and timeunit conversion
Small hint:
After the first 2424 hours, the remaining time is on January 2.2.
Big hint:
Divide 20112011 minutes by 6060.
Solution:
The remainder when 20112011 is divided by 6060 is 31.31. This means that 2011=60⋅33+31,2011 = 60 \cdot 33 + 31, which means that 20112011 minutes is the same as 3333 hours and 3131 minutes.
2424 hours takes us to January 2,2, so we get that we are 99 hours and 3131 minutes into January 2.2.
Thus, D is the correct answer.
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