2018 AMC 10A Problem 1

Problem 1 of 25EasierAlgebra

What is the value of

\left(\left((2+1)^{-1}+1\right)^{-1}+1\right)^{-1}+1?

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Solution

We can simplify this as follows.

\begin{aligned} &\left(\left((2+1)^{-1}+1\right)^{-1}+1\right)^{-1}+1 \\ &=\left(\left(\dfrac{1}{3}+1\right)^{-1}+1\right)^{-1}+1 \\ &=\left(\dfrac{3}{4}+1\right)^{-1}+1 \\ &=\dfrac{4}{7} + 1 \\ &=\dfrac{11}{7} \end{aligned}

Thus, B is the correct answer.

Concepts: fraction · order of operations

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