Difference between revisions of "2011 AMC 8 Problems/Problem 5"

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(Solution)
 
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<math>\textbf{(E)}\ \text{January 2 at 6:01PM}</math>
 
<math>\textbf{(E)}\ \text{January 2 at 6:01PM}</math>
  
==Solution==
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==Solution 1==
  
 
There are <math>60</math> minutes in an hour. <math>2011/60=33\text{r}31,</math> or <math>33</math> hours and <math>31</math> minutes. There are <math>24</math> hours in a day, so the time is <math>9</math> hours and <math>31</math> minutes after midnight on January 2, 2011. <math>\Rightarrow\boxed{\textbf{(D)}\text{ January 2 at 9:31AM}}</math>
 
There are <math>60</math> minutes in an hour. <math>2011/60=33\text{r}31,</math> or <math>33</math> hours and <math>31</math> minutes. There are <math>24</math> hours in a day, so the time is <math>9</math> hours and <math>31</math> minutes after midnight on January 2, 2011. <math>\Rightarrow\boxed{\textbf{(D)}\text{ January 2 at 9:31AM}}</math>
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==Solution 2==
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Like the previous solution, <math>2011</math> minutes is <math>33</math> hours and <math>31</math> 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 <math>\Rightarrow\boxed{\textbf{(D)}\text{ January 2 at 9:31AM}}</math>.
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-RealCXY
  
 
==See Also==
 
==See Also==
 
{{AMC8 box|year=2011|num-b=4|num-a=6}}
 
{{AMC8 box|year=2011|num-b=4|num-a=6}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 22:09, 26 October 2021

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

See Also

2011 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AJHSME/AMC 8 Problems and Solutions

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