[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 recip
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- Max@Math Revolution
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What is the harmonic mean of 20 and 30?Max@Math Revolution 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
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
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Brent
- fskilnik@GMATH
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$$? = H\left( {20,30} \right)$$Max@Math Revolution 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
$$?\,\,\, = \,\,\,{1 \over {\mu \left( {{1 \over {20}} + {1 \over {30}}} \right)}}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,{1 \over {\,\,{1 \over {24}}\,\,}}\,\,\, = \,\,\,24$$
$$\left( * \right)\,\,\,\,\,\mu \left( {{1 \over {20}} + {1 \over {30}}} \right) = {1 \over 2}\left( {{{1 \cdot 3} \over {20 \cdot 3}} + {{1 \cdot 2} \over {30 \cdot 2}}} \right) = {1 \over 2}\left( {{1 \over {3 \cdot 4}}} \right) = {1 \over {24}}$$
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)
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- Max@Math Revolution
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=>
1 / { ( 1/20 + 1/30 ) / 2 } = 1 / { ( 3/60 + 2/60 ) / 2 } = 1 / { (5/60) / 2 } = 1 / { 5 / 120 } = 120 / 5 = 24.
Therefore, the answer is B.
Answer: B
1 / { ( 1/20 + 1/30 ) / 2 } = 1 / { ( 3/60 + 2/60 ) / 2 } = 1 / { (5/60) / 2 } = 1 / { 5 / 120 } = 120 / 5 = 24.
Therefore, the answer is B.
Answer: B
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