Difference between revisions of "2016 AMC 10B Problems/Problem 3"
Doitsudoitsu (talk | contribs) m (basic solution; someone should add detailed edits in; this was rushed.) |
|||
| Line 1: | Line 1: | ||
==Problem== | ==Problem== | ||
| − | Let <math>x=-2016</math>. What is the value of <math>\ | + | Let <math>x=-2016</math>. What is the value of <math>\Bigg\vert\Big\vert |x|-x\Big\vert-|x|\Bigg\vert-x</math> ? |
<math>\textbf{(A)}\ -2016\qquad\textbf{(B)}\ 0\qquad\textbf{(C)}\ 2016\qquad\textbf{(D)}\ 4032\qquad\textbf{(E)}\ 6048</math> | <math>\textbf{(A)}\ -2016\qquad\textbf{(B)}\ 0\qquad\textbf{(C)}\ 2016\qquad\textbf{(D)}\ 4032\qquad\textbf{(E)}\ 6048</math> | ||
==Solution== | ==Solution== | ||
| − | <math> | + | Substituting carefully, <math>\Bigg\vert\Big\vert 2016-(-2016)\Big\vert-2016\Bigg\vert-(-2016)</math> |
| − | <math>4032-| | + | |
| − | <math> | + | becomes <math>|4032-2016|+2016=2016+2016=4032</math> which is <math>\textbf{(D)}</math>. |
| − | + | ||
| + | ==See Also== | ||
| + | {{AMC10 box|year=2016|ab=B|num-b=2|num-a=4}} | ||
| + | {{MAA Notice}} | ||
Revision as of 11:02, 21 February 2016
Problem
Let 
. What is the value of 
?
Solution
Substituting carefully, 
becomes 
which is 
.
See Also
| 2016 AMC 10B (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. 
