2014 AMC 10A Problem 1

Attempt Problem 1 of the 2014 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2014 AMC 10A solutions, or check the answer key.

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1.

What is the value of the following expression?

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

3

8

\dfrac{25}{2}

\dfrac{170}{3}

170

Answer: C

Concepts:fraction order of operations

Difficulty rating: 770

Small hint:

Add the fractions inside the parentheses first

Big hint:

Take the reciprocal before multiplying by

10

Solution:

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.