1. Good post? |

## GPrep Question - Task Force

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.

2. Good post? |
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?

3. Good post? |
I got 75 &#37; 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?

4. Good post? |
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.

5. Good post? |
Originally Posted by chandak_anand
.....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.

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

7. Good post? |
c it is..

8. Good post? |

There are currently 1 users browsing this thread. (0 members and 1 guests)

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•

SEO by vBSEO ©2010, Crawlability, Inc.