Hey,

My solution is:

(1) INSUFFICIENT
(2) INSUFFICIENT
In both cases we don't have enough data for variables to solve equations.

(3) COMBINE
Let's use the concept of so-called balanced value, which states that the differences between each term and the mean of the set must be equal zero.
Let's designate the number of managers as m, and the number of directors as d.
Since the average salary of the managers is 5000 less than the total average, we can boldly use -5000 as the difference between each manager's salary and the mean.
Since the average salary of the directors is 15000 grather than the total average, we can boldly use +15000 as the difference between each director's salary and the mean.
From the concept of balanced value:
15000*d+(-5000)*m=0
That is,
15000*d=5000*m; d/m=5000/15000=1/3
This ratio means that for each director in the set there are (or must be) three managers.
Therefore, the number of director is equal of 1/(1+3)=1/4 of the total number of employees. That is 25% of the total number of employees.
SUFFICIENT

The answer is C.

Thanks a lot for this instructive problem. I put in my mind one more interesting concept.

Best!

thanks for the solution and the great explanation

Hi Ed,

What is this "balanced value" concept?
I quiet frankly dont get the point.
You hav said " the differences between each term and the mean of the set must be equal zero " . dosent mean that the varience wil be 0 al the time ?

Hey Vignesh.4384,

Sorry, I'm just not able to get your point. What do you mean under the word "varience"?

The concept of "balanced value" implies exactly what I've written "the differences between each term and the mean of the set must be equal zero".
That is, if you have set of (1,2,3,4,5), the arithmetical mean of it is 3, the differences between each term and the mean of the set are (-2,-1,0,1,2), and the sum of them is zero. That's it!

I hope this clarification is barely intelligible.

Best!