2014 AMC 10A Problems/Problem 1

The following problem is from both the 2014 AMC 12A #1 and 2014 AMC 10A #1, so both problems redirect to this page.

Problem

What is $10 \cdot \left(\tfrac{1}{2} + \tfrac{1}{5} + \tfrac{1}{10}\right)^{-1}?$

$\textbf{(A)}\ 3\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ \frac{25}{2}\qquad\textbf{(D)}}\ \frac{170}{3}\qquad\textbf{(E)}\ 170$ (Error compiling LaTeX. Unknown error_msg)

Solution

Sum the fractions over the common denominator: $\dfrac{1}{2}+\dfrac15+\dfrac1{10}=\dfrac{5+2+1}{10}=\dfrac45$

Now the answer is just some arithmetic: $10\cdot\left(\dfrac45\right)^{-1}=10\cdot\dfrac{5}{4}=\boxed{\textbf{(C)}\ \dfrac{25}2}$

2014 AMC 10A (Problems • Answer Key • Resources)
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All AMC 10 Problems and Solutions

2014 AMC 12A (Problems • Answer Key • Resources)
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All AMC 12 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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2014 AMC 10A Problems/Problem 1

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