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In Cytherea Corporation, each employee was given an interper

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In Cytherea Corporation, each employee was given an interper [#permalink] New post 04 Dec 2017, 03:05
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In Cytherea Corporation, each employee was given an interpersonal assessment with a score from 0 to 60. Te average score among all male employees was 35, and the average score for all employees was 39. If Cytherea Corporation has 40 male employees and 10 female employees, what was the average score among all female employees?

A. 40
B. 43
C. 47
D. 51
E. 55

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Re: In Cytherea Corporation, each employee was given an interper [#permalink] New post 04 Dec 2017, 05:51
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The standard, mathematical approach (should take not more than a minute, quicker if you're good with mental math):

Total score of the male employees = 35 * 40
Total score of the female employees = x * 10

\(Overall\,average = \frac{total\,score\,of\,males\,+\,total\,score\,of\,females}{total\,number\,of\,employees}\)

\(39 = \frac{35\,*\,40 + x\,*\,10}{50}\)

Divide the equation by 10,

\(39 * 5 = 35 * 4 + x\)

\(x = 39 * 5 - 35 * 4\)

\(x = 55\)

Alternatively, using a higher level of logic and reduced math: The mean of all males is 35. The mean of all employees is 39 (this does not mean the mean of all females is 43 because the number of females is not the same as that of males). This difference of 4 would equate to the same difference from the mean female score (let's say y). The weighted difference for males is 4 * 40. But we have 10 female employees, so 4 * 40 = 10 * x where x is the additional female score. It turns out to be 16, so the mean female score is 39 + 16 = 55.
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Re: In Cytherea Corporation, each employee was given an interper   [#permalink] 04 Dec 2017, 05:51
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In Cytherea Corporation, each employee was given an interper

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