At a certain company, average (arithmetic mean)number of

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

(1) Definitely not sufficient, we don't know neither the number of women, nor the combined average for the company.

(2) Sufficient. The combined average being 9.3, the differences form this average are 0.5 and 0.2, therefore the ratio between the male and female employees is 0.2:0.5=2:5.

Answer B

This is a question involving weighted average.
Having two quantities \(Q_1\) and \(Q_2\) with averages \(a_1\) and \(a_2\) respectively, if the combined average is \(a\), and let assume that \(a_1>a>a_2,\) then we can write:

\(\frac{a_1Q_1+a_2Q_2}{Q_1+Q_2}=a\) from which \(a_1Q_1+a_2Q_2=aQ_1+aQ_2\) or \((a_1-a)Q_1=(a-a_2)Q_2,\) which means that the distances from the combined average are inversely proportional to the quantities.
This equality we can also be written as \(\frac{a_1-a}{a-a_2}=\frac{Q_2}{Q_1}.\)

In the above question, the differences were 0.5 and 0.2 (men's average to women's average differences), which give a ratio of 5:2, then the quantities (numbers of employees) are in a ratio of 2:5 (male to women).
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We can use alligations for such kind of problems

Let us assume the number of male employees in the company is m and number of female employees is f. Average number of years of experience for male employees is 9.8 and average number of years of experience for female employees is 9.1.
We need the ratio m:f.

Statement 1: m = 52
This is not enough to determine the ratio of m:f.

Not sufficient.

Statement 2: (9.8m + 9.1f)/(m + f) = 9.3
--> 9.8m + 9.1f = 9.3m + 9.3f.
--> 0.5m = 0.2f
--> m/f = m : f = 2:5

Sufficient

The correct answer is B.
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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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