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We define the average (harmonic mean) as the reciprocal of the average

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We define the average (harmonic mean) as the reciprocal of the average  [#permalink]

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New post 02 Jun 2017, 01:19
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We define the average (harmonic mean) as the reciprocal of the average (arithmetic mean) of reciprocals. What is the average (harmonic mean) of 2, 3, and 6?

A. 1/3
B. 1/2
C. 1
D. 2
E. 3

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Re: We define the average (harmonic mean) as the reciprocal of the average  [#permalink]

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New post 02 Jun 2017, 02:00
1
Harmonic mean = 1/A

A ==> Average of the reciprocals of 2, 3 and 6 = (1/2 + 1/3 + 1/6)/3 = 1/3

Hence H = 3 Answer option E.
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Re: We define the average (harmonic mean) as the reciprocal of the average  [#permalink]

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New post 02 Jun 2017, 23:16
MathRevolution wrote:
We define the average (harmonic mean) as the reciprocal of the average (arithmetic mean) of reciprocals. What is the average (harmonic mean) of 2, 3, and 6?

A. 1/3
B. 1/2
C. 1
D. 2
E. 3


Average (Arithmetic mean) of reciprocals of 2,3 and 6 = \((\frac{1}{2} + \frac{1}{3} + \frac{1}{6}) /3\) = \((\frac{3+2+1}{6})/3\) = \((\frac{6}{6})/3\) = \(\frac{1}{3}\)

Harmonic mean is the reciprocal of the average (arithmetic mean) of reciprocals = \(\frac{3}{1}\) = 3
Answer E...
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Re: We define the average (harmonic mean) as the reciprocal of the average  [#permalink]

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New post 04 Jun 2017, 03:36
MathRevolution wrote:
We define the average (harmonic mean) as the reciprocal of the average (arithmetic mean) of reciprocals. What is the average (harmonic mean) of 2, 3, and 6?

A. 1/3
B. 1/2
C. 1
D. 2
E. 3


\(\frac{1}{2} + \frac{1}{3} + \frac{1}{6} =
\frac{3}{h}\)
h = 3, answer E
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Re: We define the average (harmonic mean) as the reciprocal of the average  [#permalink]

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New post 04 Jun 2017, 17:56
==> If you find the average of the reciprocals, you get \(\frac{++}{3}=\frac{1}{3}\) .

Since it is the reciprocal of that, the answer is E.
Answer: E
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Re: We define the average (harmonic mean) as the reciprocal of the average  [#permalink]

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New post 04 Jun 2017, 23:46
Reciprocal of the - average of reciprocals.

So lets take average of reciprocals first. (1/2 + 1/3 + 1/6)/3 = (6/6)/3 = 1/3

Now lets take its reciprocal. 1/(1/3) = 3. hence E answer
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Re: We define the average (harmonic mean) as the reciprocal of the average  [#permalink]

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New post 22 Jan 2019, 17:09
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Re: We define the average (harmonic mean) as the reciprocal of the average   [#permalink] 22 Jan 2019, 17:09
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