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

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<math>42</math> days after January 1 is <math>\fbox{\textbf{(E) }\text{February 12}}</math>
 
<math>42</math> days after January 1 is <math>\fbox{\textbf{(E) }\text{February 12}}</math>
 
Keep in mind that you start on January 1st so you can't count it as a day. By the time you get to noon on January 31, only 30 days have past. Them you can continue counting like you normally would to February 12.  
 
Keep in mind that you start on January 1st so you can't count it as a day. By the time you get to noon on January 31, only 30 days have past. Them you can continue counting like you normally would to February 12.  
   ~Nosysnow | wonsysoN~
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   ~Nosysnow
 
 
  
 
== See Also ==
 
== See Also ==

Revision as of 19:47, 16 February 2018

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?

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

Solution 1

There are $10!$ seconds that the blood has before expiring and there are $60 \cdot 60 \cdot 24$ seconds in a day. Dividing $\frac{10!}{60 \cdot 60 \cdot 24}$ gives $42$ days. $42$ days after January 1 is $\fbox{\textbf{(E) }\text{February 12}}$.

Solution 2

$10! = 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1$. Convert $10!$ seconds to minutes: $9\cdot 8\cdot 7\cdot 5\cdot 4\cdot 3\cdot 2$ minutes. Convert minutes to hours: $9\cdot 8\cdot 7\cdot 2$ hours. Convert hours to days: $3\cdot 7\cdot 2 = 42$ days.

$42$ days after January 1 is $\fbox{\textbf{(E) }\text{February 12}}$ Keep in mind that you start on January 1st so you can't count it as a day. By the time you get to noon on January 31, only 30 days have past. Them you can continue counting like you normally would to February 12.

  ~Nosysnow

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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