2016 AMC 12B Problem 2

Attempt Problem 2 of the 2016 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2016 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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?

$2$

$45$

$504$

$1008$

$2015$

Answer: A

Concepts:harmonic mean fraction estimation

Difficulty rating: 1020

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.

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