Hard GMAT Question

ronibr · Posted: Thu Jul 19, 2007 12:04 pm Post subject: Hard GMAT Question

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

blah45 · Posted: Thu Jul 19, 2007 7:35 pm Post subject:

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%