AMC12 2016 B

AMC12 2016 B · Q2

AMC12 2016 B · Q2. It mainly tests Fractions, Rounding & estimation.

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?

两个数的调和平均数可以用“它们的积的两倍除以它们的和”来计算。$1$ 和 $2016$ 的调和平均数最接近哪个整数？

(A) 2 2

(B) 45 45

(D) 1008 1008

(E) 2015 2015

Answer

Correct choice: (A)

正确答案：（A）

Solution

Answer (A): The harmonic mean of 1 and 2016 is $$ \frac{2\cdot 1\cdot 2016}{1+2016}=2\cdot\frac{2016}{2017}\approx 2\cdot 1=2. $$

答案（A）：1 和 2016 的调和平均数为 $$ \frac{2\cdot 1\cdot 2016}{1+2016}=2\cdot\frac{2016}{2017}\approx 2\cdot 1=2。 $$

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