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2016 AMC 12B Problem 2

Problem 2 of 25EasierProbability & StatisticsArithmetic

The harmonic mean of two numbers can be computed as twice their product divided by their sum. The harmonic mean of 11 and 20162016 is closest to which integer?

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Solution

The harmonic mean is 2⋅1⋅20161+2016=40322017.\dfrac{2\cdot1\cdot2016}{1+2016}=\dfrac{4032}{2017}. Since 20162017\dfrac{2016}{2017} is very close to 1,1, this is just under 2,2, so the closest integer is 2.2. Thus, the correct answer is A.
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Tagged: harmonic mean · fraction · estimation

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