2011 AMC 8 Problem 5

Below is the professionally curated solution for Problem 5 of the 2011 AMC 8, 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.

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Concepts:date and time unit conversion

Difficulty rating: 770

What time was it $2011$ minutes after the beginning of January $1,$ $2011?$

January $1$ at $9:31$ PM

January $1$ at $11:51$ PM

January $2$ at $3:11$ AM

January $2$ at $9:31$ AM

January $2$ at $6:01$ PM

Solution:

The remainder when $2011$ is divided by $60$ is $31.$ This means that $2011 = 60 \cdot 33 + 31,$ which means that $2011$ minutes is the same as $33$ hours and $31$ minutes.

$24$ hours takes us to January $2,$ so we get that we are $9$ hours and $31$ minutes into January $2.$

Thus, D is the correct answer.

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