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06 Feb 2019, 08:14
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
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Question Stats:
82% (01:24) correct
18%
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wrong
based on 132
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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
Updated on: 17 May 2021, 07:23
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.
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MathRevolution
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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06 Feb 2019, 08:35
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MathRevolution
\(? = H\left( {20,30} \right)\)
\(?\,\,\, = \,\,\,{1 \over {\mu \left( {{1 \over {20}} + {1 \over {30}}} \right)}}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,{1 \over {\,\,{1 \over {24}}\,\,}}\,\,\, = \,\,\,24\)
\(\left( * \right)\,\,\,\,\,\mu \left( {{1 \over {20}} + {1 \over {30}}} \right) = {1 \over 2}\left( {{{1 \cdot 3} \over {20 \cdot 3}} + {{1 \cdot 2} \over {30 \cdot 2}}} \right) = {1 \over 2}\left( {{1 \over {3 \cdot 4}}} \right) = {1 \over {24}}\)
The correct answer is therefore (B).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
