# Difference between revisions of "2018 AMC 8 Problems/Problem 10"

## Problem 10

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?

$\textbf{(A) }\frac{3}{7}\qquad\textbf{(B) }\frac{7}{12}\qquad\textbf{(C) }\frac{12}{7}\qquad\textbf{(D) }\frac{7}{4}\qquad \textbf{(E) }\frac{7}{3}$

## Solution

The sum of the reciprocals is $\frac 11 + \frac 12 + \frac 14= \frac 74$. Their average is $\frac 7{12}$. Taking the reciprocal of this gives $\boxed{\textbf{(C) }\frac{12}{7}}$