1986 AMC 8 Problem 5

Attempt Problem 5 of the 1986 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 1986 AMC 8 solutions, or check the answer key.

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

5.

A contest began at noon one day and ended 10001000 minutes later. At what time did the contest end?
10 ⁣: ⁣0010\!:\!00 p.m.
midnight
2 ⁣: ⁣302\!:\!30 a.m.
4 ⁣: ⁣404\!:\!40 a.m.
6 ⁣: ⁣406\!:\!40 a.m.
Answer: D
Concepts:date and timeunit conversion
Small hint:
Convert 10001000 minutes into hours and minutes by dividing by 6060
Big hint:
10001000 minutes is 1616 hours and 4040 minutes; add that to noon
Solution:
Since 10001000 minutes =100060= \dfrac{1000}{60} hours =1623= 16\dfrac23 hours =16= 16 hours 4040 minutes, the contest ended 1616 hours 4040 minutes past noon, which is 4 ⁣: ⁣404\!:\!40 a.m.
Thus, the correct answer is D .
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