Difference between revisions of "2018 AMC 10A Problems/Problem 3"
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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 in <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 in <math>\fbox{\textbf{(E) }\text{February 12}}</math>. | ||
+ | ==Solution 2 (Consise) | ||
+ | |||
+ | There are <math>60 \cdot 60 \cdot 24 = 86400</math> seconds in a day, and so <math>10! \div 86400 = 42</math> days. Since there are <math>31</math> days in January (consult a calendar), then <math>42-31+1</math> (Jan 1 doesn't count) is <math>12</math> days into February, so <math>\boxed{\textbf{(E) }\text{February 12}}</math>. | ||
~nosysnow ~Max0815 | ~nosysnow ~Max0815 | ||
Revision as of 09:37, 28 September 2022
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 dividing by again: 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 in .
==Solution 2 (Consise)
There are seconds in a day, and so days. Since there are days in January (consult a calendar), then (Jan 1 doesn't count) is days into February, so . ~nosysnow ~Max0815
Video Solutions
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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 |
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