2018 AMC 8

Complete problem set with solutions and individual problem pages

Problem 10 Easy

The harmonic mean of a set of non-zero numbers is the reciprocal of the average of the reciprocals of the numbers. What is the harmonic mean of 1, 2, and 4?

  • A.

    \frac{3}{7}

  • B.

    \frac{7}{12}

  • C.

    \frac{12}{7}

  • D.

    \frac{7}{4}

  • E.

    \frac{7}{3}

Answer:C

The sum of the reciprocals is \frac{1}{1} + \frac{1}{2} + \frac{1}{4}= \frac{7}{4}. Their average is \frac{7}{12}. Taking the reciprocal of this gives \boxed{\textbf{(C) }\frac{12}{7}}.

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