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

Revision as of 16:05, 16 June 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?

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

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

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

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.

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