Hi All,

This DS question is ultimately about Weighted Averages.

We're told that the average work experience (at a particular company) for men is 9.8 years and the average work experience for women is 9.1 years. We're asked for the RATIO of Men to Women at this company.

In these types of question, we don't necessarily need the number of men and the number of women to find the ratio of men to women...

Fact 1: 52 males work at the company.

This tells us nothing about the number of women working at the company.
Fact 1 is INSUFFICIENT.

Fact 2: The average work experience for ALL employees is 9.3 years.

Using this Fact, and the information in the prompt, I'm going to set up a Weighted Average calculation:

M = # of male employees
F = # of female employees

(9.8M + 9.1F)/(M+F) = 9.3

9.8M + 9.1F = 9.3M + 9.3F
0.5M = 0.2F

5M = 2F

At this point, if you recognize that we have a ratio, then you can stop working. If you want to do the next "math step", then that's fine though...

M/F = 2/5

We now have the ratio that we're asked for.
Fact 2 is SUFFICIENT.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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We can use alligations for such kind of problems

OA:B

Let Number of Male be \(M\), and number of females be \(F\)

\(Av_{Male}\) and \(Av_{Female}\) be average number of years of experience of male and female respectively.

Given : \(Av_{Male} = 9.8\quad years ,Av_{Female}=9.1\quad years\)

We have to find the ratio \(\frac{M}{F}\)

Statement 1: There are 52 male employees at the company

It gives us value of \(M\), But We do not have value of \(F\).

So Statement 1 alone is insufficient to find the ratio \(\frac{M}{F}\)

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

\(\frac{M*Av_{Male}+F*Av_{Female}}{M+F}=9.3\)

\(9.8M+9.1F=9.3(M+F)\)

Dividing both sides by \(F\), we get

\(9.8\frac{M}{F}+9.1=9.3(\frac{M}{F}+1)\)

We can find the value of \(\frac{M}{F}\)

Statement 2 alone is sufficient
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