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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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We define the average (harmonic mean) as the reciprocal of the average  [#permalink]

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02 Jun 2017, 00:19
1
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Difficulty:

55% (hard)

Question Stats:

44% (01:05) correct 56% (00:59) wrong based on 88 sessions

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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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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 27 Nov 2016 Posts: 4 Re: We define the average (harmonic mean) as the reciprocal of the average [#permalink] ### Show Tags 02 Jun 2017, 01:00 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. Director Joined: 04 Dec 2015 Posts: 740 Location: India Concentration: Technology, Strategy Schools: ISB '19, IIMA , IIMB, XLRI WE: Information Technology (Consulting) Re: We define the average (harmonic mean) as the reciprocal of the average [#permalink] ### Show Tags 02 Jun 2017, 22:16 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... Manager Joined: 19 Aug 2015 Posts: 88 Location: India GMAT 1: 650 Q49 V30 Re: We define the average (harmonic mean) as the reciprocal of the average [#permalink] ### Show Tags 04 Jun 2017, 02:36 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 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6985 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: We define the average (harmonic mean) as the reciprocal of the average [#permalink] ### Show Tags 04 Jun 2017, 16:56 ==> 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: We define the average (harmonic mean) as the reciprocal of the average  [#permalink]

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04 Jun 2017, 22:46
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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22 Jan 2019, 16:09
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Re: We define the average (harmonic mean) as the reciprocal of the average   [#permalink] 22 Jan 2019, 16:09
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