2014 AMC 12A Problem 1

Problem 1 of 25EasierAlgebra

What is

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

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Solution

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.

Concepts: fraction · exponent

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.