Ratios - from GMATPrep 1

[ruthm_24]

At a certain company, the average (arithmetic mean) number of years of experience is 9.8 years for the male employees and 9.1 years for the female employees. What is the ratio of the number of the company's male employees to the number of the company's female employees?

1. There are 52 male employees at the company.

2. The average number of years of experience for the company's male and female employees combined is 9.3 years.

Answer is B but I can't figure out why.

Thanks in advance.

[this_time_i_will]

explanation for B:
from the question we know that:
SUM(EME) = 9.8m...where, SUM(EME) means sum of the experience of male employees, and m is no. of males.
SUM(EFE) = 9.1f

from B:
[SUM(EME)+SUM(EFE)]/m+f = 9.3
[9.8m+9.1f] = 9.3 (m+f)..solve this eqn for getting a ratio of m/f.

[hi.itz.mani]

let Ym1 be the Year of experience of Male 1 and similarly Yf1 be the year of experience of Female 1

As per the problem statement = (Ym1 + ......YmN) / N = 9.8
= sum( Year of experience of all males ) = 9.8 N ..................(1)

Similarly sum ( Year of experience of all females ) = 9.1 M .........................(2)

Questions is to Find N / M ?

Statement 1 N = 52 ... but with this we can't find the ration of N / M .... hence insuffiecient

Statement 2 sum ( Year of experience of male + female ) = 9.3 ( N + M) ................... (3)

If we add equation 1 and 2 we get

sum ( years of experience of male + female ) = 9.1 M + 9.8 N = 9.3(N+ M) ( From equation 3)

hence 9.1 M + 9.8 N = 9.3 N + 9.3 M

From the above equation we can get the ration of N / M . hence statement 2 is sufficient .

Answer is B