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Each employee on a certain task force is either a manager or

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Director
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Each employee on a certain task force is either a manager or [#permalink] New post 03 Apr 2007, 18:37
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 average ( arithmetic mean ) salary of the managers on the task force is $5,000 less than the average salary of all the employees on the task force.

(2) The average ( arithmetic mean ) salary of the directors on the task force is $15,000 greater than the average salary of all the employees on the task force.


Please explain why the answer is "C". how can we solve this question using both the statements (1) and (2)?
VP
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 [#permalink] New post 03 Apr 2007, 19:56
Do a search in this forum. It has been posted thousands of times.
Director
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Please Help [#permalink] New post 03 Apr 2007, 20:09
I tried searching for it in the forum, but unable to locate it. Would be very kind of you, if you could give me the link or let me know the explanation
Director
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Power Prep Question [#permalink] New post 03 Apr 2007, 21:01
Could anyone please explain?
VP
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 [#permalink] New post 03 Apr 2007, 21:15
Director
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Solution..I solved it [#permalink] New post 03 Apr 2007, 21:56
Managers Directors
Number of people X Y
Average Salary M D


we need to find out Y/(X+Y)


from 1) we have

M+5000 = ( M*X+D*Y)/(X+Y)

=> M*X+M*Y+5000*X+5000*Y = M*X+D*Y

=> M*Y+5000*X+5000*Y = D*Y

=> 5000*X+5000*Y = D*Y-M*Y

=> 5000(X+Y) = D*Y-M*Y

=> 5000 = (D-M)*Y /(X+Y)

You don't know (D-M)---- thus (1) alone is insufficient


from 2) we have

D-15000 = ( M*X+D*Y)/(X+Y)

=> D*X+D*Y-15000*X-15000*Y = M*X+D*Y

=> D*X-15000*X-15000*Y = M*X

=> D*X-M*X = 15000*(X+Y)

=> X*(D-M) = 15000*(X+Y)

=> 15000 = (D-M)*X /(X+Y)

You don't know (D-M)---- thus (2) alone is insufficient



now solving for both 1) and 2)


Add both the results of (1) and (2)

(5000+15000) = { (D-M)*Y + (D-M)*X }/ ( X+Y )

=> 20000 = (D-M)*(X + Y ) /(X+Y)

=> 20000 = (D-M)

Putting the value of ( D-M ) in the equation (1) will give us;

5000 = 20000*Y /(X+Y)

=>Y/(X+Y) = 5000/20000


Thus using (1) and (2) we could solve it.


Therefore the answer is ( C )[/list][/list]
Solution..I solved it   [#permalink] 03 Apr 2007, 21:56
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