Difference between revisions of "2016 AMC 12A Problems/Problem 3"
(Created page with "==Solution== <cmath>\text{rem}\left(\frac{3}{8},-\frac{2}{5}\right)</cmath> <cmath>=\frac{3}{8}-\left(-\frac{2}{5}\right)\lfloor\frac{\frac{3}{8}}{-\frac{-2}{5}}\rfloor</cmath...") |
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<cmath>=\frac{3}{8}-\frac{2}{5}</cmath> | <cmath>=\frac{3}{8}-\frac{2}{5}</cmath> | ||
<cmath>=\boxed{\textbf{(B)}-\frac{1}{40}}</cmath> | <cmath>=\boxed{\textbf{(B)}-\frac{1}{40}}</cmath> | ||
| + | Notice that it would not matter if either <math>-\frac{2}{5}</math> or <math>\frac{2}{5}</math> were used. | ||
Revision as of 22:15, 3 February 2016
Solution
![\[\text{rem}\left(\frac{3}{8},-\frac{2}{5}\right)\]](http://latex.artofproblemsolving.com/4/b/c/4bc95cf8469a4cfdb6d3b62fdf68c7f9a237ba3b.png)
![\[=\frac{3}{8}-\left(-\frac{2}{5}\right)\lfloor\frac{\frac{3}{8}}{-\frac{-2}{5}}\rfloor\]](http://latex.artofproblemsolving.com/9/e/2/9e2ec5d9d9a299a5209531556bb07324cb949a79.png)
![\[=\frac{3}{8}+\left(\frac{2}{5}\right)\lfloor -\frac{15}{16}\rfloor\]](http://latex.artofproblemsolving.com/2/d/c/2dc3f5e57674267596d5d36a4c2291bcf1e6eca1.png)
![\[=\frac{3}{8}+\left(\frac{2}{5}\right)\left(-1\right)\]](http://latex.artofproblemsolving.com/c/e/1/ce191ca7c81c2c3d36c3c92798070445a4a58ca3.png)
![\[=\frac{3}{8}-\frac{2}{5}\]](http://latex.artofproblemsolving.com/0/e/8/0e82baa90861d265d469d327e817acadd6168a85.png)
![\[=\boxed{\textbf{(B)}-\frac{1}{40}}\]](http://latex.artofproblemsolving.com/f/f/e/ffe2006d31961de958874647aa4dcb4b583657fd.png)
Notice that it would not matter if either 
or 
were used.
