Difference between revisions of "2018 AMC 10A Problems/Problem 3"
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| + | == Problem == | ||
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A unit of blood expires after <math>10!=10\cdot 9 \cdot 8 \cdots 1</math> seconds. Yasin donates a unit of blood at noon of January 1. On what day does his unit of blood expire? | A unit of blood expires after <math>10!=10\cdot 9 \cdot 8 \cdots 1</math> seconds. Yasin donates a unit of blood at noon of January 1. On what day does his unit of blood expire? | ||
<math>\textbf{(A) }\text{January 2}\qquad\textbf{(B) }\text{January 12}\qquad\textbf{(C) }\text{January 22}\qquad\textbf{(D) }\text{Febuary 11}\qquad\textbf{(E) }\text{Febuary 12}</math> | <math>\textbf{(A) }\text{January 2}\qquad\textbf{(B) }\text{January 12}\qquad\textbf{(C) }\text{January 22}\qquad\textbf{(D) }\text{Febuary 11}\qquad\textbf{(E) }\text{Febuary 12}</math> | ||
| − | < | + | == 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{Febuary 12}}</math>. | ||
| + | |||
| + | == Solution 2 == | ||
| − | <math>10! = 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1</math> | + | <math>10! = 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1</math>. |
| − | Convert <math>10!</math> seconds to minutes: <math>9\cdot 8\cdot 7\cdot 5\cdot 4\cdot 3\cdot 2</math> minutes | + | Convert <math>10!</math> seconds to minutes: <math>9\cdot 8\cdot 7\cdot 5\cdot 4\cdot 3\cdot 2</math> minutes. |
Convert minutes to hours: <math>9\cdot 8\cdot 7\cdot 2</math> hours. | Convert minutes to hours: <math>9\cdot 8\cdot 7\cdot 2</math> hours. | ||
Convert hours to days: <math>3\cdot 7\cdot 2 = 42</math> days. | Convert hours to days: <math>3\cdot 7\cdot 2 = 42</math> days. | ||
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<math>42</math> days after January 1 is <math>\fbox{\textbf{(E) }\text{Febuary 12}}</math> | <math>42</math> days after January 1 is <math>\fbox{\textbf{(E) }\text{Febuary 12}}</math> | ||
| − | ~Nosysnow | + | ~Nosysnow | wonsysoN~ |
== See Also == | == See Also == | ||
Revision as of 21:04, 8 February 2018
Contents
Problem
A unit of blood expires after 
seconds. Yasin donates a unit of blood at noon of January 1. On what day does his unit of blood expire?
Solution 1
There are 
seconds that the blood has before expiring and there are 
seconds in a day. Dividing 
gives 
days. days after January 1 is 
.
Solution 2
.
Convert seconds to minutes: 
minutes.
Convert minutes to hours: 
hours.
Convert hours to days: 
days.
days after January 1 is
~Nosysnow | wonsysoN~
See Also
| 2018 AMC 10A (Problems • Answer Key • Resources) | ||
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
