GPrep Question - Task Force

[Gruesomeguy]

Each employee on a certain task force is either a manager or a director. What percent of the employee force are directors?

• The average (arithmetic mean) salary of the managers on the task force is 5,000 less than the average salary of all employees on the task force.

• The average (arithmetic mean) salary of the directors on the task force is 15,000 greater than the average salary of all employees on the task force.

Please Post Explanations as well.

[vbhup2]

It is obvious that (1) and (2) are INSUFFICIENT alone.

Have a feeling it is C, so trying to solve combining (1) and (2)

Let the avg sal of all employees, managers and directors be A,M and D respectively.

We know that A = Sum of sal of M's + Sum of Sal of D's / Nm + Nd where Nm and Nd represent the no. of managers and no. of directors. ------ Eq (1)

M = A - 5000 --------- Eq (2)
D = A + 15,000 -------- Eq (3)
Let X be the ratio of managers to all employees
So, 1 - X will be the ratio of directors to all employees

=> Sum of Sal of M = M * X * (Nm + Nd)
=> Sum of Sal of D = D * (1-X) * (Nm + Nd)

Substituting these values in Eq (1)

A = [M * X * (Nm + Nd) + D * (1-X) * (Nm+ Nd)] / (Nm + Nd)
A = M*X + D*(1-X)

Using Eq (2) and Eq (3)

A = X * (A-5000) + (1-X) * (A + 15000)
A = AX - 5000X + A + 15000 -AX - 15000X

=> 20000X = 15000
=> X = 3/4

Thus the % of Managers = 75% . Hence, C.

Took a lot of time to solve... this one. I probably would've guessed this one as C on the actual exam.

Does anybody have an easier method?

[chandak_anand]

I got 75 % too, my method is equally long

Let M = Sum of salaries of Manager, D = Sum of salaries of director
m = No of Manager n= No of Director

From 1 ==> (M + D)/(m +d) - M/m = 5000

From 2 ===> D/d - (M + D)/(m + d) = 15,000

so from 1 ===> Mm + dm - Mm - Md = 5000m(m +d) ==>(3)
and from 2 ==> Dm + Dd -Md - Dd = 15000d(m +d) ===>(4)

equating values of (m + d) from the eqn 3 & 4

(Dm - Md)/(5000m) = (Dm - Md)/(15,000d)

which gives m = 3d, so the manager is 75% and Director is 25%

Hence C.(Took me 5 mins..)

Can anybody suggest a better method?

[ben928]

Hint: you don't have to solve it out. If you understand the concept and can assume you would be able to figure it out, you should choose C and go on.

[soulasylum]

.....Can anybody suggest a better method?

Great way of solving !.. Thanks Vbup and anand !. Wouldn't it also help to plug in numbers and solve the problem.. I mean, we are looking at a 2 minute time frame to get the solution to the problem, aren't we?? Just trying out the plug in method below..Statements 1 and 2 by themselves aren't sufficient, because we would require the total salaries of Managers/Directors/Team to solve the question.Now, plugging in numbers and taking both the statements together..Assuming, avg(M) = 1000, then avg(total team)=6000 (from Statement 1)If avg(total team)=6000, avg (D) = 21000 (from Statement 2)Assuming, m is the number of managers and d is the number of directors. (mx1000)+(dx21000)=(m+d)x6000 (Equating the total salary)15000d = 5000m . Therefore m/d = 3. Componento : m+d /d = (3+1) / 1 = 4. Therefore d/(m+d) = 1/4 or 25%. (Ratio of directors to total task force)Hence answer C.

[soulasylum]

Apologies for the lack of formatting in my above post.. Just not sure whats wrong.. Nevertheless, hope it makes sense !

[kaushikt]

c it is..

[Gruesomeguy]

C is the Official Answer