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

We are given that the average (arithmetic mean) number of years of experience is 9.8 years for male employees and 9.1 years for the female employees. We are asked to determine the ratio of the number of the company's male employees and the number of the company's female employees.

Of course, if we know the number of male employees and the number of female employees, we can determine that ratio.

Statement One Alone:

There are 52 male employees at the company.

Since we don't know the number of female employees at the company, we can't determine the ratio of the number of male employees to the number of female employees. Statement one alone is not sufficient.

Statement Two Alone:

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

Let the number of male employees be m and the number of female employees be f.

Since the average years of experience of the male employees is 9.8, the sum is 9.8m. Similarly, the same quantity for the females is 9.1f. So, the sum for the males and females combined is 9.8m + 9.1f. Dividing this by the total number of employees (which is m + f) gives us the overall average number of years of experience, which we are told is 9.3:

(9.8m + 9.1f)/(m+f) = 9.3

9.8m + 9.1f = 9.3m + 9.3f

0.5m = 0.2f

m/f = 2/5

Statement two alone is sufficient.

Answer: B

Let the total years of male = x
Let the total years of female = y
Let the males = m
Let the females = f
Question; What is the ratio of the number of the company's male employees to the number of the company's female employees?
$$\frac{x}{m}\ =\ 9.8\ $$
= x = 9.8m
$$\frac{y}{f}\ =\ 9.1\ $$
= y = 9. 1f

Statement 1 ;
There are 52 male employees at the company. The information given is not enough to relate the male with the female employees hence statement 1 is not sufficient.

Statement 2 ;
The average number of years of experience for the company's male and female employees combined is 9.3 years.
$$\frac{\left(x\ +\ y\right)}{m\ +\ f}=\ 9.3$$
Remember that x = 9.8m and y = 9.1f
$$\frac{\left(9.8m\ +\ 9.1f\right)}{m\ +\ f}\ =\ 9.3$$
9.8m + 9.1f = 9.3m + 9.3f
9.8m - 9.3m = 9.3f - 9.1f
$$\frac{0.5m}{f\ }=\ \frac{0.2f}{f}$$
$$\frac{0.5m}{f}\ =\ 0.2$$
$$\frac{m}{f\ }=\ \frac{0.2}{0.5}$$

Statement 2 is suficient.
Option B is the correct answer.