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# We define the harmonic mean of a set of numbers as the reciprocal of t

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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We define the harmonic mean of a set of numbers as the reciprocal of t  [#permalink]

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06 Feb 2019, 07:14
00:00

Difficulty:

35% (medium)

Question Stats:

58% (01:33) correct 42% (01:41) wrong based on 12 sessions

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[GMAT math practice question]

We define the harmonic mean of a set of numbers as the reciprocal of the average (arithmetic mean) of the reciprocals of the numbers. What is the harmonic mean of 20 and 30?

A. 22
B. 24
C. 25
D. 26
E. 28

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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" CEO Joined: 11 Sep 2015 Posts: 3435 Location: Canada Re: We define the harmonic mean of a set of numbers as the reciprocal of t [#permalink] ### Show Tags 06 Feb 2019, 07:34 Top Contributor MathRevolution wrote: [GMAT math practice question] We define the harmonic mean of a set of numbers as the reciprocal of the average (arithmetic mean) of the reciprocals of the numbers. What is the harmonic mean of 20 and 30? A. 22 B. 24 C. 25 D. 26 E. 28 What is the harmonic mean of 20 and 30? NOTE: 20 = 20/1 So, the reciprocal of 20 = 1/20 And the reciprocal of 30 = 1/30 The average of 1/20 and 1/30 = (1/20 + 1/30 )/2 = (3/60 + 2/60 )/2 = (5/60 )/2 = (5/60 )/(2/1) = (5/60 )(1/2) = 5/120 The reciprocal of 5/120 = 120/5 = 24 Answer: B Cheers, Brent RELATED VIDEO FROM MY COURSE _________________ Test confidently with gmatprepnow.com GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 750 Re: We define the harmonic mean of a set of numbers as the reciprocal of t [#permalink] ### Show Tags 06 Feb 2019, 07:35 MathRevolution wrote: [GMAT math practice question] We define the harmonic mean of a set of numbers as the reciprocal of the average (arithmetic mean) of the reciprocals of the numbers. What is the harmonic mean of 20 and 30? A. 22 B. 24 C. 25 D. 26 E. 28 $$? = H\left( {20,30} \right)$$ $$?\,\,\, = \,\,\,{1 \over {\mu \left( {{1 \over {20}} + {1 \over {30}}} \right)}}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,{1 \over {\,\,{1 \over {24}}\,\,}}\,\,\, = \,\,\,24$$ $$\left( * \right)\,\,\,\,\,\mu \left( {{1 \over {20}} + {1 \over {30}}} \right) = {1 \over 2}\left( {{{1 \cdot 3} \over {20 \cdot 3}} + {{1 \cdot 2} \over {30 \cdot 2}}} \right) = {1 \over 2}\left( {{1 \over {3 \cdot 4}}} \right) = {1 \over {24}}$$ The correct answer is therefore (B). We follow the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net VP Joined: 09 Mar 2018 Posts: 1000 Location: India Re: We define the harmonic mean of a set of numbers as the reciprocal of t [#permalink] ### Show Tags 06 Feb 2019, 07:37 MathRevolution wrote: [GMAT math practice question] We define the harmonic mean of a set of numbers as the reciprocal of the average (arithmetic mean) of the reciprocals of the numbers. What is the harmonic mean of 20 and 30? A. 22 B. 24 C. 25 D. 26 E. 28 (1/20 + 1/30)/2 = 5/60 = 1/12*2, average of this Reciprocal of this term = 24 B _________________ If you notice any discrepancy in my reasoning, please let me know. Lets improve together. Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6967 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: We define the harmonic mean of a set of numbers as the reciprocal of t [#permalink] ### Show Tags 08 Feb 2019, 01:40 => $$1 / { ( \frac{1}{20} + \frac{1}{30} ) / 2 } = 1 / { ( \frac{3}{60} + \frac{2}{60} ) / 2 } = 1 / { (\frac{5}{60}) / 2 } = 1 / { \frac{5}{120} } = \frac{120}{5} = 24.$$ Therefore, the answer is B. Answer: B _________________ 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 harmonic mean of a set of numbers as the reciprocal of t   [#permalink] 08 Feb 2019, 01:40
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