Difference between revisions of "2016 AMC 10B Problems/Problem 3"

m (basic solution; someone should add detailed edits in; this was rushed.)
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==Problem==
 
==Problem==
  
Let <math>x=-2016</math>. What is the value of <math>\bigg|</math> <math>|x|-x|-|x|</math> <math>\bigg|</math> <math>-x</math>?
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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>|-2016|-(-2016) \implies 2016+2016 \implies 4032</math>.
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Substituting carefully, <math>\Bigg\vert\Big\vert 2016-(-2016)\Big\vert-2016\Bigg\vert-(-2016)</math>
<math>4032-|-2016| \implies 4032-2016 \implies 2016</math>.
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<math>|2016|=2016</math>.
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becomes <math>|4032-2016|+2016=2016+2016=4032</math> which is <math>\textbf{(D)}</math>.
<math>2016-(-2016) \implies 2016+2016=\boxed{4032}</math>.
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==See Also==
 +
{{AMC10 box|year=2016|ab=B|num-b=2|num-a=4}}
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{{MAA Notice}}

Revision as of 11:02, 21 February 2016

Problem

Let $x=-2016$. What is the value of $\Bigg\vert\Big\vert |x|-x\Big\vert-|x|\Bigg\vert-x$ ?

$\textbf{(A)}\ -2016\qquad\textbf{(B)}\ 0\qquad\textbf{(C)}\ 2016\qquad\textbf{(D)}\ 4032\qquad\textbf{(E)}\ 6048$

Solution

Substituting carefully, $\Bigg\vert\Big\vert 2016-(-2016)\Big\vert-2016\Bigg\vert-(-2016)$

becomes $|4032-2016|+2016=2016+2016=4032$ which is $\textbf{(D)}$.

See Also

2016 AMC 10B (ProblemsAnswer KeyResources)
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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