Difference between revisions of "2018 AMC 10A Problems/Problem 3"

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Education, the Study of Everything
 
Education, the Study of Everything
  
 
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== Solution ==
== Solution 1 ==
 
There are <math>10!</math> seconds that the blood has before expiring and there are <math>60 \cdot 60 \cdot 24</math> seconds in a day. Dividing <math>\frac{10!}{60 \cdot 60 \cdot 24}</math> gives <math>42</math> days. <math>42</math> days after January 1 is <math>\fbox{\textbf{(E) }\text{February 12}}</math>.
 
 
 
== Solution 2 ==
 
  
 
The problem says there are <math>10! = 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1</math> seconds.
 
The problem says there are <math>10! = 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1</math> seconds.

Revision as of 11:01, 29 November 2020

Problem

A unit of blood expires after $10!=10\cdot 9 \cdot 8 \cdots 1$ seconds. Yasin donates a unit of blood at noon of January 1. On what day does his unit of blood expire?

$\textbf{(A) }\text{January 2}\qquad\textbf{(B) }\text{January 12}\qquad\textbf{(C) }\text{January 22}\qquad\textbf{(D) }\text{February 11}\qquad\textbf{(E) }\text{February 12}$

Video Solution

https://youtu.be/bPfLeXu9kx0

Education, the Study of Everything

Solution

The problem says there are $10! = 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1$ seconds. Convert $10!$ seconds to minutes by dividing by $60$: $9\cdot 8\cdot 7\cdot 5\cdot 4\cdot 3\cdot 2$ minutes. Convert minutes to hours by again, dividing by $60$: $9\cdot 8\cdot 7\cdot 2$ hours. Convert hours to days by dividing by $24$: $3\cdot 7\cdot 2 = 42$ days.

Now we need to count $42$ days after January 1. Since we start on Jan. 1, then we can't count that as a day itself. When we reach Jan. 31(The end of the month), we only have counted 30 days. $42 - 30 = 12$. Count $12$ more days, resulting $\fbox{\textbf{(E) }\text{February 12}}$

~nosysnow and Max0815

Video Solution

https://youtu.be/vO-ELYmgRI8

https://youtu.be/FbSYTL8tPwo

~savannahsolver

See Also

2018 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
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 AMC 10 Problems and Solutions

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