Difference between revisions of "2017 AMC 8 Problems/Problem 24"
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Revision as of 14:01, 22 November 2017
Problem 24
Mrs. Sanders has three grandchildren, who call her regularly. One calls her every three days, one calls her every four days, and one calls her every five days. All three called her on December 31, 2016. On how many days during the next year did she not receive a phone call from any of her grandchildren?
Solution
In 
days, there are ![\[360 \cdot \frac 23 \cdot \frac 34 \cdot \frac 45 = 144\]](http://latex.artofproblemsolving.com/6/7/8/6783f07de26963cc58034fd375274930f3d2ae9a.png)
days without calls. Also note that in the last five days of the year, day 
and 
also do not have any calls. Thus our answer is 
.
~nukelauncher
See Also
| 2017 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 23 |
Followed by Problem 25 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
