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We define the harmonic mean of a set of numbers as the reciprocal of
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06 Feb 2019, 08:14
06 Feb 2019, 08:14
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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
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
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Updated on: 17 May 2021, 07:23
Updated on: 17 May 2021, 07:23
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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
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
Originally posted by BrentGMATPrepNow on 06 Feb 2019, 08:34.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:23, edited 1 time in total.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:23, edited 1 time in total.
Re: We define the harmonic mean of a set of numbers as the reciprocal of
[#permalink]
06 Feb 2019, 08:35
06 Feb 2019, 08:35
Expert Reply
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
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.
