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

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

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New post 06 Feb 2019, 08:14
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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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Re: We define the harmonic mean of a set of numbers as the reciprocal of t  [#permalink]

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New post 06 Feb 2019, 08:34
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

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Re: We define the harmonic mean of a set of numbers as the reciprocal of t  [#permalink]

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New post 06 Feb 2019, 08:35
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.
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Re: We define the harmonic mean of a set of numbers as the reciprocal of t  [#permalink]

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New post 06 Feb 2019, 08:37
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
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Re: We define the harmonic mean of a set of numbers as the reciprocal of t  [#permalink]

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New post 08 Feb 2019, 02:40
=>

\(1 / { ( \frac{1}{20} + \frac{1}{30} ) / 2 } = 1 / { ( \frac{3}{60} + \frac{2}{60} ) / 2 } = 1 / { (\frac{5}{60}) / 2 } = 1 / { \frac{5}{120} } = \frac{120}{5} = 24.\)

Therefore, the answer is B.
Answer: B
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Re: We define the harmonic mean of a set of numbers as the reciprocal of t   [#permalink] 08 Feb 2019, 02:40
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