2018 AMC 10 A

Complete problem set with solutions and individual problem pages

Problem 1 Easy

What is the value of \left(\left((2+1)^{-1}+1)^{-1}+1\right)^{-1}\right)+1? (2018 AMC 10A Problem, Question#1)

  • A.

    \frac{5}{8}

  • B.

    \frac{11}{7}

  • C.

    \frac{8}{5}

  • D.

    \frac{18}{11}

  • E.

    \frac{15}{8}

Answer:B

We will start with 2+1=3 and then apply the operation"invert and add one" three times. These iterations yield (after 3): \frac{4}{3},\frac{7}{4} , and finally (\rm B) \frac{11}{7}.

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