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2010 AMC 12B Problems/Problem 24

Revision as of 16:31, 12 July 2010 by Lg5293 (talk | contribs) (Created page with '== Problem 24 == The set of real numbers <math>x</math> for which <cmath>\dfrac{1}{x-2009}+\dfrac{1}{x-2010}+\dfrac{1}{x-2011}\ge1</cmath> is the union of intervals of the for…')
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Problem 24

The set of real numbers $x$ for which

\[\dfrac{1}{x-2009}+\dfrac{1}{x-2010}+\dfrac{1}{x-2011}\ge1\]

is the union of intervals of the form $a<x\le b$. What is the sum of the lengths of these intervals?

$\textbf{(A)}\ \dfrac{1003}{335} \qquad \textbf{(B)}\ \dfrac{1004}{335} \qquad \textbf{(C)}\ 3 \qquad \textbf{(D)}\ \dfrac{403}{134} \qquad \textbf{(E)}\ \dfrac{202}{67}$

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