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

$$? = H\left( {20,30} \right)$$
$$?\,\,\, = \,\,\,{1 \over {\mu \left( {{1 \over {20}} + {1 \over {30}}} \right)}}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,{1 \over {\,\,{1 \over {24}}\,\,}}\,\,\, = \,\,\,24$$
$$\left( * \right)\,\,\,\,\,\mu \left( {{1 \over {20}} + {1 \over {30}}} \right) = {1 \over 2}\left( {{{1 \cdot 3} \over {20 \cdot 3}} + {{1 \cdot 2} \over {30 \cdot 2}}} \right) = {1 \over 2}\left( {{1 \over {3 \cdot 4}}} \right) = {1 \over {24}}$$

The correct answer is therefore (B).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

=>

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