Difference between revisions of "2016 AMC 12B Problems/Problem 2"

(See Also)
(Solution)
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==Solution==
 
==Solution==
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Since the harmonic mean is <math>2</math> times their product divided by their sum, we get the equation
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<math>\frac{2\times1\times2016}{1+2016}</math>
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which is then
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<math>\frac{4032}{2017}</math>
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which is finally closest to <math>\boxed{\textbf{(A)}\ 2}</math>.
  
 
==See Also==
 
==See Also==
 
{{AMC12 box|year=2016|ab=B|num-b=1|num-a=3}}
 
{{AMC12 box|year=2016|ab=B|num-b=1|num-a=3}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 11:11, 21 February 2016

Problem

The harmonic mean of two numbers can be calculated as twice their product divided by their sum. The harmonic mean of $1$ and $2016$ is closest to which integer?

$\textbf{(A)}\ 2 \qquad \textbf{(B)}\ 45 \qquad \textbf{(C)}\ 504 \qquad \textbf{(D)}\ 1008 \qquad \textbf{(E)}\ 2015$

Solution

Since the harmonic mean is $2$ times their product divided by their sum, we get the equation

$\frac{2\times1\times2016}{1+2016}$

which is then

$\frac{4032}{2017}$

which is finally closest to $\boxed{\textbf{(A)}\ 2}$.

See Also

2016 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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 AMC 12 Problems and Solutions

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