2014 AMC 10A Problem 1

We get that $$\begin{aligned} &\dfrac{1}{2} + \dfrac{1}{5} + \dfrac{1}{10} \\ &= \dfrac{5}{10} + \dfrac{2}{10} + \dfrac{1}{10} \\&= \dfrac{4}{5}. \end{aligned}$$ Then $\left(\dfrac{4}{5}\right)^{-1} = \dfrac{5}{4}$ and then finally, $$10 \cdot \dfrac{5}{4} = \dfrac{25}{2}.$$ Thus, C is the correct answer.