GMATPrep question on DS - average

M- NO OF MANAGER
D- NO OF DIRECTORS
E-NO OF EMPLOYEES
Let MAVG be managers avg salary
Let EMPAVG be employees average slaary
Let DIREAVG be directors avg salary

FORMAULA IS : (MAVG*M + DIRAVG*D) / M+D = EMPAVG (1)

To find ratio of M/D from which we can find the percent by multipying by 100

Stmt I

MAVG = EMPAVG-5000 (2)

cant find ratio m/n with this
INSUFF

Stmt II

DAVG = EMPAVG+15000 (3)

cant find ratio m/n with this
INSUFF

Stmt I and II together

Substitute in (1),

MAVG = EMPAVG-5000 FROM (2) AND DAVG = EMPAVG+15000 (3)

(MAVG*M + DIRAVG*D) / M+D = EMPAVG

= ((EMPAVG-5000)*M + (EMPAVG+15000)*D) / M+D = EMPAVG (CROSS MULTIPLY M+D GOES TO RIGHT HAND SIDE)

= M-EMPAVG -5000M + D-EMPAVG+15000D = M-EMPAVG + D-EMPAVG (M-EMPAVG AND D-EMPAVG ON BOTH SIDES CANCEL OUT)

15000D = 5000M

M/D = 3/1 This is part to part ratio(manager to director ratio) which is telling us that for every 3 managers there is 1 director

Part to whole ratio for manager will be 3/4 i.e 3/4*100 = 75%


Not needed but just to show:

Part to whole ratio for directors will be 1/4 i.e 1/4*100 = 25%

Skyline,

In Jackcrystal's link u will see Sudhir's solution which is using weighted average but my approach above would be an algebric one(also using weighted average in my foruma (1)).

Either one is good and go with whichever(may be both also) u can understand better and will be able to apply in future problems.

I have tried to explain as best as I could but let me know if u still have questions.

Regards,
Cramya

cramya wrote:Skyline,

In Jackcrystal's link u will see Sudhir's solution which is using weighted average but my approach above would be an algebric one(also using weighted average in my foruma (1)).

Either one is good and go with whichever(may be both also) u can understand better and will be able to apply in future problems.

I have tried to explain as best as I could but let me know if u still have questions.

Regards,
Cramya

Thanks Cramya. I have a clear picture now.

Regards,
skyline