# 2011 AMC 8 Problems/Problem 5

## Problem

What time was it $2011$ minutes after midnight on January 1, 2011? $\textbf{(A)}\ \text{January 1 at 9:31PM}$ $\textbf{(B)}\ \text{January 1 at 11:51PM}$ $\textbf{(C)}\ \text{January 2 at 3:11AM}$ $\textbf{(D)}\ \text{January 2 at 9:31AM}$ $\textbf{(E)}\ \text{January 2 at 6:01PM}$

## Solution 1

There are $60$ minutes in an hour. $2011/60=33\text{r}31,$ or $33$ hours and $31$ minutes. There are $24$ hours in a day, so the time is $9$ hours and $31$ minutes after midnight on January 2, 2011. $\Rightarrow\boxed{\textbf{(D)}\text{ January 2 at 9:31AM}}$

## Solution 2

Like the previous solution, $2011$ minutes is $33$ hours and $31$ minutes. That means it has to be January 1 at 9:31PM or January 2 at 9:31AM because they are the only ones that end with 31. But, the answer can’t be in January 1 because there are 24 hours in a day and 33 is greater than 24. So, the answer is $\Rightarrow\boxed{\textbf{(D)}\text{ January 2 at 9:31AM}}$.

-RealCXY

## Solution 3 (Estimate)

The answer choices are relatively far apart, so we can use estimation to solve this problem. $2100/60$ is around $35$ hours, or about $1.5$ days. The only answer choice around $1.5$ days from the midnight of January 1, 2011 is $\boxed{\textbf{(D)}\text{ January 2 at 9:31AM}}$.

MegaBoy6679 :D 23:31, 26 December 2022 (EST)

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 