Difference between revisions of "2018 AMC 10A Problems/Problem 3"
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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{February 11}\qquad\textbf{(E) }\text{February 12}</math> | <math>\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}</math> | ||
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| − | == Solution | + | == Solution == |
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. | ||
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Now we need to count <math>42</math> 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. <math>42 - 30 = 12</math>. Count <math>12</math> more days, resulting <math>\fbox{\textbf{(E) }\text{February 12}}</math> | Now we need to count <math>42</math> 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. <math>42 - 30 = 12</math>. Count <math>12</math> more days, resulting <math>\fbox{\textbf{(E) }\text{February 12}}</math> | ||
~nosysnow and Max0815 | ~nosysnow and Max0815 | ||
| + | |||
| + | ==Video Solutions== | ||
| + | https://youtu.be/vO-ELYmgRI8 | ||
| + | |||
| + | https://youtu.be/FbSYTL8tPwo | ||
| + | |||
| + | ~savannahsolver | ||
| + | |||
| + | https://youtu.be/bPfLeXu9kx0 | ||
| + | |||
| + | Education, the Study of Everything | ||
== See Also == | == See Also == | ||
Revision as of 18:53, 29 November 2020
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
The problem says there are 
seconds.
Convert 
seconds to minutes by dividing by 
: 
minutes.
Convert minutes to hours by again, dividing by : 
hours.
Convert hours to days by dividing by 
: 
days.
Now we need to count 
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. 
. Count 
more days, resulting 
~nosysnow and Max0815
Video Solutions
~savannahsolver
Education, the Study of Everything
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. 
