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

Revision as of 12:53, 18 January 2021

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

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.

Revision as of 18:31, 23 December 2018 (view source) Tiblis (talk \| contribs) (→‎Solution) ← Older edit		Revision as of 12:53, 18 January 2021 (view source) Etvat (talk \| contribs) Newer edit →
Line 1:		Line 1:
−	==Problem 10==	+	==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?		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?

Page

Toolbox

Search

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

Revision as of 12:53, 18 January 2021

Problem

Solution

See Also