What is 10 × ((1)/(2) + (1)/(5) + (1)/(10))^-1?

2014 AMC 12A Problem 1

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What is

10 \cdot \left(\dfrac{1}{2} + \dfrac{1}{5} + \dfrac{1}{10}\right)^{-1}?

3

8

\dfrac{25}{2}

\dfrac{170}{3}

170

Add the three fractions inside the parentheses first

\dfrac12+\dfrac15+\dfrac{1}{10}=\dfrac{8}{10}

, then take the reciprocal and multiply by

10

The sum inside the parentheses is

\dfrac12+\dfrac15+\dfrac{1}{10}=\dfrac{5+2+1}{10}=\dfrac{4}{5}.

Its reciprocal is

\dfrac54,

so the expression equals

10\cdot\dfrac54=\dfrac{25}{2}.

Thus, the correct answer is C.