2016 AMC 12B Problem 2

Problem 2 of 25EasierAlgebra

The harmonic mean of two numbers can be computed as twice their product divided by their sum. The harmonic mean of

1

and

2016

is closest to which integer?

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Solution

The harmonic mean is

\dfrac{2\cdot1\cdot2016}{1+2016}=\dfrac{4032}{2017}.

Since

\dfrac{2016}{2017}

is very close to

1,

this is just under

2,

so the closest integer is

2.

Thus, the correct answer is A.

Concepts: harmonic mean · fraction · estimation

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.