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

Latest revision as of 17:35, 25 December 2023

Problem

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

Video Solution (CRITICAL THINKING!!!)

https://youtu.be/v-ZooJaqrWA

~Education, the Study of Everything

Video Solution by OmegaLearn

https://youtu.be/TkZvMa30Juo?t=2935

~ pi_is_3.141592653589793238462643383279502884197

Video Solution

https://youtu.be/PA9X-2xLuxY

~savannahsolver

2018 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 9	Followed by Problem 11
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AJHSME/AMC 8 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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