Directors %?

The answer here will be E.

From statement (1), we get:

SalMan*NumMan = SalAll*NumAll - 5000

If we could figure out both NumMan and NumAll, then we could find out the percentage that are directors. It would be 100% - (NumMan/NumAll). However, we have 4 unknowns and one equation, so we are unable to solve for NumMan. Statement (1) is not sufficient.

From statement (2) we get:

SalDir*NumDir = SalAll*NumAll + 15000

We have too many unknowns to calculate NumDir/NumAll, so statement (2) is insufficient on its own.

We can take each of these equations, though, and solve for SalAll*NumAll. We then get:

SalMan*NumMan + 5000 = SalAll*NumAll and

SalDir*NumDir - 15000 = SallAll*NumAll.

Setting them equal we get:

SalMan*NumMan + 5000 = SalDir*NumDir - 15000

As you can see, from this statement we are only going to be able to get NumDir/(NumMan+NumDir) in terms of other variables. We don't have enough information to solve, so the answer is E.

Best wishes,

Tatiana

That's what I thought.. but the answer is C and this question is from GMAT prep... so I guess there is some trick...

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

1). The avg salary of the managers on the task force is $5000 less than
the avg salary of all employees on the task force.

2). The avg salary of the directors on the task force is $15000 greater than
the avg salary of all employees on the task force.

You can determine the weights of 2 groups from a weighted average.

Let's look at a number line:

Avg salary manager ---5000--- avg salary all ---------15000---------avg salary director

So, the average salary is 1/4 of the way between managers and directors. The only way this can be true if there are 3 times as many managers as directors; therefore, 75% are managers.

There's a simple formula you can use in these situations:

#groupa : #groupb = (distance from avg group b):(distance from avg group a)

In this question, we get:

#a:#b = 15000:5000 = 3:1

The reason that the # of equation # of unknowns rule (my all time favourite DS rule, by the way) doesn't apply here is that we're not solving for the value of one of the variables; rather, we're solving for the relationship a:b. When one is solving for a relationship, one can often get away with fewer than the usual # of equations.

let us suppose that there are 'a' mangers and 'b' directors. Let 'x' be the average of the salaries of all the employees of the task force. Let y be the average salary of the directors.

Then according to the statement I .................. (x-5) is the average salary of the Managers.

therefore {a(x-5) + b*y} = x*(a+b)
this simplifies to b*(y-x) = 5000a
but this statement alone is not sufficient to get the ratio of a/b.


Statement II alone is also not sufficent ( similar equation could be established). This statement says (y-x) = 15000


but taking both statements we can establish that b/a = 1/3

Lets assume the average of all emp is A, number of managers is M and number of directors as D. We only need to find the proportion of managers to directors to find the %age of directors.

Total salary disbursed = Ax(M+D)

From (a) salary given to only managers = (A-5000)xM
From (b) salary given to only directors = (A+15000)xD

But, total salary given = salary given to managers + salary given to directors

=> Ax(M+D) = (A-5000)xM + (A+15000)xD
=> AM + AD = AM - 5000M + AD + 15000D
=> 5000M = 15000D
=> M : D is equal to 3 : 1
=> Directors form 1/4 of the total population (25%)
Hence answer is [C]

Thank you all...