2018 AMC 10A Problems/Problem 1

Problem

What is the value of \[\left(\left((2+1)^{-1}+1\right)^{-1}+1\right)^{-1}+1?\] $\textbf{(A) } \frac58 \qquad \textbf{(B) }\frac{11}7 \qquad \textbf{(C) } \frac85 \qquad \textbf{(D) } \frac{18}{11} \qquad \textbf{(E) } \frac{15}8$

Solution

\[\left(\left((2+1)^{-1}+1\right)^{-1}+1\right)^{-1}+1\] \[=\left(\left(3)^{-1}+1\right)^{-1}+1\right)^{-1}+1\] \[=\left(\left(\frac{1}{3}+1\right)^{-1}+1\right)^{-1}+1\] \[=\left(\left(\frac{4}{3}\right)^{-1}+1\right)^{-1}+1\] \[=\left(\frac{3}{4}+1\right)^{-1}+1\] \[=\left(\frac{7}{4}\right)^{-1}+1\] \[=\frac{4}{7}+1\] \[=\frac{11}{7}\] Therefore, the answer is $\boxed{\textbf{(B) } \frac{11}{7} }$.

Video Solution

https://youtu.be/vO-ELYmgRI8

See Also

2018 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
First Problem
Followed by
Problem 2
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All AMC 10 Problems and Solutions

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