S_a - Average salary of all employees
S_m - Average salary for manager
S_d - Average salary of directors
d - # of directors;
m - # of managers.
Question \frac{d}{m+d}=?

(1) S_m=S_a-5000 --> Not sufficient to calculate ratio.
(2) S_d=S_a+15000 --> Not sufficient to calculate ratio.

(1)+(2) S_a=\frac{S_m*m+S_d*d}{d+m} --> substitute S_m and S_d --> S_a=\frac{(S_a-5000)*m+(S_a+15000)*d}{d+m} --> S_a*d+S_a*m=S_a*m-5000*m+S_a*d+15000*d --> S_a*d and S_a*m cancel out --> m=3d --> \frac{d}{m+d}=\frac{d}{3d+d}=\frac{1}{4}. Sufficient.

Answer: C.

Or for (1)+(2): if we say that the fraction of the directors is x (x=\frac{d}{d+m}) then the fraction of the managers will be (1-x) (1-x=\frac{m}{d+m}) --> S_a=x(S_a+15000)+(1-x)(S_a-5000) --> S_a=x*S_a+15000x+S_a-5000-x*S_a+5000x --> x=\frac{1}{4}.
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In a work force, the employees are either managers or directors. What is the percentage of directors?
(1) the average salary for manager is $5,000 less than the total average salary.
(2) the average salary for directors is $15,000 more than the total average salary.


c

One has to understand the concept of weighted averages pretty well to understand my solution.

The point of a weighted average is to know how much weight to give these two individual groups, the managers and the directors.

Statement 1 tells how the managers' salaries relate to employee average but there is no information about how the directors' salaries relate to the employee average.
Insufficient
Eliminate A & D

Statement 2 tells how the directors' salaries relate to employee average but there is no information about how the managers' salaries relate to the employee average.
Insufficient
Eliminate B

Statements 1 and 2 together:
The manager average is 5000 less than the combined average. The director average is 15000 greater than the combined average. The difference between the manager average and the director average is 20000.

If there were an equal number of managers and directors they would each be 10000 off of the combined average - that would be a 50/50 weighting.
But the combined average is closer to the manager average, so there are more managers than directors. Use the above three numbers to know how much: the difference is 20000, and the combined average is three-quarters of the way towards the manager average.

Hence, 3/4 of the employees are managers & 1/4 are directors.
Sufficient.

Hence C.
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This can be solved in allegations method.
The ratio of the components is inverse of the ratio of their differences from the average.

#Managers:#Directors = Difference between salary between combined avg and directors : Difference between salary between combined avg and managers

M:D = 15000:500 = 3:1

D:M = 1:3

D:(M+D) = 1: (1+3) = 1:4

this way you can solve under 30 secs.
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Press Kudos, if I have helped.
Thanks!

Let's call all employee A, manager M, and director D, so A=M+D. Their average salary is Sa, Sm, and Sd for A, M, and D respectively. The percentage of M and D are x% and y% respectively, so x+y=100%. We have the following equation:
Sa=\frac{x*Sm+y*Sd}{x+y} or Sa=\frac{x*Sm+y*Sd}{100}
Now consider the statement 1, it can be written as Sm=Sa-5000, not sufficient to determine x and y.
The same for statement 2, it leads to Sd=Sa+15000, not sufficient to determine x and y.
Nevertheless, using both statement, by eliminating the constant as follows:
3Sm+Sd=3*(Sa-5000)+(Sa+15000)
3Sm+Sd=4Sa
Sa=\frac{3Sm+Sd}{4}=Sa=\frac{75Sm+25Sd}{100}

Answer is C.
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Hardworkingly, you like my post, so kudos me.

From the given, avg salary = (D(X%) + M(100-X%))/100

Statement 1 doesn't provide any info on D. Not Sufficient
Statement 2 doesn't provide any info on M. Not Sufficient

Now we have 3 unknowns - with 2 equations...

Statement 1 & Statement 2 can come together to provide us with our 3rd equation, which is, on avg, M = D - 20,000

With 3 equations and 3 unknowns - u can find M, D & X. Sufficient

Answer: C
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Kudos always appreciated if my post helped you

Bunuel - is my minimalist solution of just identifying 3 equations satisfactory?

Or do you recommend fully solving it out to see if I net a result?
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Kudos always appreciated if my post helped you

Good question. While you can not figure out the number of manager and directors available, you still can manipulate the two equations to get a ratio or percentage. I didn't do any calculations but knowing that there where two statements that are relative to one another and that has factors that do not cancel one another out when setting up the equation to solve for the ratio is enough to conclude that C is the answer.

Good one.

To solve it under 2 minutes, I had to guess this one as C. You are provided two relationships: managers-all and directors-all. That should be likely enough to determine the number of managers and directors as note that the differences in average numbers are specific to the number of managers and directors.

To calculate, you can solve two equations such as:
1. Sm/m = (Sm+Sd)/(m+d) - 5000.
2. Sd/d = (Sm+Sd)/(m+d) + 15000.

You need to solve for d/m+d.
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Hey Bunuel,

What clue told you that "average salary of all the employees", your S_alpha was a weighted average?I tried solving the problem thinking it was an arithmetic average. Was the clue that the question did not specify that it was an arithmetic? Just puzzled. I mean it makes sense that its a weighted average but the question did not specify that info.