Data Sufficiency

Please help me with this problem.
Each employee on a task force is either a manager or a director.What percentage of the employee on the task force are directors?

1) Arithmatic mean salary of the managers on the task force is $5000 less than the average salary of all employees on the task force.

2) Arithmatic mean salary of the directors on the task force is $15000 more than the average
salary of all employees on the task force.

OA after some discussion.

mukgera wrote:Please help me with this problem.
Each employee on a task force is either a manager or a director.What percentage of the employee on the task force are directors?

1) Arithmatic mean salary of the managers on the task force is $5000 less than the average salary of all employees on the task force.

2) Arithmatic mean salary of the directors on the task force is $15000 more than the average
salary of all employees on the task force.

OA after some discussion.

The ratio of managers to directors is 3. Is this correct???

Cheers
Ami/-

the OA is C..But i don't know the approach.If anyone can help then it would be wonderful.

gmatclubmember wrote:

mukgera wrote:Please help me with this problem.
Each employee on a task force is either a manager or a director.What percentage of the employee on the task force are directors?

1) Arithmatic mean salary of the managers on the task force is $5000 less than the average salary of all employees on the task force.

2) Arithmatic mean salary of the directors on the task force is $15000 more than the average
salary of all employees on the task force.

OA after some discussion.

The ratio of managers to directors is 3. Is this correct???

Cheers
Ami/-

[spoiler][/spoiler]

Let there be 'a' no. of managers having salary M and
let there be 'b' no. of directors having salary D.

1. (aM+bD)/(a+b) - M = 5000.
We cannot deduce the ratio of a and b with this information.
2. (aM+bD)/(a+b)+15000 = D.
We cannot deduce the ration of a and b with this information.

Now lets consider both together:
we get a/b=3, (managers to directors is 3).

Hence C.

Cheers
Ami/-

Consider there are M number of managers with salary s1 and D numbers of directors s2.

From 1st statement we get s1= (M*s1 + D*s2)/(M+D) -5000. simplifying we get D(S2-s1) = 5000.
so it is insufficient

From 2nd statement we get s2= (M*s1 + D*s2)/(M+D) + 15000. Simplifying we get M(s2 - s1) = 15000.

so this is insufficient.

combing the equation when we divide we get D/M = 1/3

Add 1 to both side 1 + D/M = 1+1/3

(M+D)/M = 4/3
reverse it and you will get M/(M+D) = 3/4

Hey thanks for the explanation.

mukgera wrote:Please help me with this problem.
Each employee on a task force is either a manager or a director.What percentage of the employee on the task force are directors?

1) Arithmatic mean salary of the managers on the task force is $5000 less than the average salary of all employees on the task force.

2) Arithmatic mean salary of the directors on the task force is $15000 more than the average
salary of all employees on the task force.

OA after some discussion.

This is a weighted average question.
The managers are being combined with the directors to form a mixture of managers and directors.
We can use alligation, which dictates the following:

The proportion of each element in the mixture is equal to the distance between the average attributed to the other element in the mixture and the average attributed to the entire mixture.

Directors:
The proportion of directors in the mixture = the distance between the average salary of the MANAGERS (the other element in the mixture) and the average salary of all the employees (the entire mixture).
This information is provided by Statement 1: The average salary of the managers on the task force is $5000 less than the average salary of all the employees on the task force.

Managers:
The proportion of managers in the mixture = the distance between the average salary of the DIRECTORS (the other element in the mixture) and the average salary of all the employees (the entire mixture).
This information is provided by Statement 2: The average salary of the directors on the task force is $15000 more than the average salary of all the employees on the task force.

Combining the statements:
Proportion of directors : proportion of managers = 5000:15000 = 1:3.

Thus, of every 4 employees, 1 is a director:
1/4 = 25%.
Sufficient.

The correct answer is C.

A very very important question to understand. Just allot the parameters or alphabets for each and every value without solving deeper into it...

I think this would be the most easy question because of that... No need for formula and no need for the calculations as well ...

Just simple averages being used and that is it....

Let there be 'a' no. of managers having salary M and
let there be 'b' no. of directors having salary D.

1. (aM+bD)/(a+b) - M = 5000.
We cannot deduce the ratio of a and b with this information.
2. (aM+bD)/(a+b)+15000 = D.
We cannot deduce the ration of a and b with this information.


Combination is a system of linear equations in 2 variables which is solvable.
(C) is answer.

I marked E in my pactice test, please let me know what mistake did I commit

let there is D directors with the Total salary of S1
and M managers with total salary of S2

Statement 1: S2 / M = {(S1 + S2) / (M + D)} - 5000 --- Insufficient
Statement 2: S1 / D = {(S1 + S2) / (M + D)} + 15000 --- Insufficient

Combining both the statements and subtracting 1st from 2nd, i get

S1/D - S2/M = 20000 -- This gives me 4 unknown variables and we can not find the ratio of D / (D+M)
hence i chose the ans E

where did i go wrong?