Hi there,
I came across this question, has no clue.
Thanks for any help ....
Each employee on a certain task is either a manager or a director. What percent of the employees on the task force are directors?
1. The average (arithmetic mean) salary of the managers on the task force is 5000 less then the average of all employees on the task force
2. The average (arithmetic mean) salary of the directors on the task force is 15000 greater then the average of all employees on the task force
1. Statement 1 is sufficient
2. Statement 2 is sufficient
3. Both statements are sufficient , but neither alone
4. Each statement is sufficient
5. Statements 1 and 2 are not sufficient
Hard GMAT Question
This topic has expert replies
Let's say...
Ms - sum of manager's salary
Mt - total number of managers
Ds - sum of directors
Dt - total number of directors
As - all employee salary
At - total number of employees
So, As = Ms + Ds
At = Mt + Dt
We're asked to find ratio of Dt/At = ?
(1)
Ms/Mt = (As/At) - 5000
Ms/Mt = [(Ms + Ds)/(Mt + Dt)] - 5000 (sub. As = Ms + Ds, At = Mt + Dt)
solving,
DsMt - MsDt = 5000Mt(Mt + Dt)
INSUFF
(2)
Ds/Dt = (As/At) + 15000
Ds/Dt = [(Ds + Ms)/ (Mt + Dt)] + 15000
solving,
DsMt - MsDt = 15000Dt(Mt + Dt)
INSUFF
Together...
5000Mt = 15000Dt
so, Mt = 3Dt
that is already enough to calculate the desire ratio.... Ans (C)
just to complete the problem... Dt/At = Dt/(Mt + Dt) = 1/4 => 25%
Ms - sum of manager's salary
Mt - total number of managers
Ds - sum of directors
Dt - total number of directors
As - all employee salary
At - total number of employees
So, As = Ms + Ds
At = Mt + Dt
We're asked to find ratio of Dt/At = ?
(1)
Ms/Mt = (As/At) - 5000
Ms/Mt = [(Ms + Ds)/(Mt + Dt)] - 5000 (sub. As = Ms + Ds, At = Mt + Dt)
solving,
DsMt - MsDt = 5000Mt(Mt + Dt)
INSUFF
(2)
Ds/Dt = (As/At) + 15000
Ds/Dt = [(Ds + Ms)/ (Mt + Dt)] + 15000
solving,
DsMt - MsDt = 15000Dt(Mt + Dt)
INSUFF
Together...
5000Mt = 15000Dt
so, Mt = 3Dt
that is already enough to calculate the desire ratio.... Ans (C)
just to complete the problem... Dt/At = Dt/(Mt + Dt) = 1/4 => 25%