Difference between revisions of "2018 AMC 10A Problems/Problem 1"

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What is the value of
 
What is the value of
 
<cmath>\left(\left((2+1)^{-1}+1\right)^{-1}+1\right)^{-1}+1?</cmath>
 
<cmath>\left(\left((2+1)^{-1}+1\right)^{-1}+1\right)^{-1}+1?</cmath>
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<math>\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 </math>
 
<math>\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 </math>
  
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Therefore, the answer is <math>\boxed{\textbf{(B) } \frac{11}{7} }</math>.
 
Therefore, the answer is <math>\boxed{\textbf{(B) } \frac{11}{7} }</math>.
  
==Video Solution==
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== Video Solutions ==
 
https://youtu.be/vO-ELYmgRI8
 
https://youtu.be/vO-ELYmgRI8
  
==Video Solution 2==
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https://youtu.be/cat3yTIpX4k
https://youtu.be/Ns34Jiq9ofc
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—DSA_Catachu
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~savannahsolver
  
 
== See Also ==
 
== See Also ==
 
 
{{AMC10 box|year=2018|ab=A|before=First Problem|num-a=2}}
 
{{AMC10 box|year=2018|ab=A|before=First Problem|num-a=2}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 01:45, 19 October 2020

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 Solutions

https://youtu.be/vO-ELYmgRI8

https://youtu.be/cat3yTIpX4k

~savannahsolver

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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