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

(Created page with "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 expir...")
 
(Added the brute-force solution)
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<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>
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<h2>Solution</h2>
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<math>10! = 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1</math>
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Convert <math>10!</math> seconds to minutes: <math>9\cdot 8\cdot 7\cdot 5\cdot 4\cdot 3\cdot 2</math> minutes
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Convert minutes to hours: <math>9\cdot 8\cdot 7\cdot 2</math> hours.
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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>

Revision as of 13:24, 8 February 2018

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?

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

Solution

$10! = 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1$ 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 $\fbox{\textbf{(E) }\text{Febuary 12}}$

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