SAT Math Practice Question #24717 - SATify | SATify

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SAT Math Practice Question #24717 - SATify | SATify

#24717

algebra

inequalities

hard

150 sec

The set of real numbers $x$ for which

$\frac{1}{x - 2009} + \frac{1}{x - 2010} + \frac{1}{x - 2011} \geq 2$

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

A.

$\frac{1}{2}$

B.

$1$

C.

$\frac{3}{2}$

D.

$2$

E.

$\frac{5}{2}$