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

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Director
Joined: 03 Sep 2006
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Each employee on a certain task force is either a manager or [#permalink]

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03 Apr 2007, 18:37
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
Joined: 25 Jun 2006
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03 Apr 2007, 19:56
Do a search in this forum. It has been posted thousands of times.
Director
Joined: 03 Sep 2006
Posts: 879
Followers: 6

Kudos [?]: 772 [0], given: 33

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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
Joined: 03 Sep 2006
Posts: 879
Followers: 6

Kudos [?]: 772 [0], given: 33

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03 Apr 2007, 21:01
VP
Joined: 25 Jun 2006
Posts: 1172
Followers: 3

Kudos [?]: 148 [0], given: 0

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03 Apr 2007, 21:15
Director
Joined: 03 Sep 2006
Posts: 879
Followers: 6

Kudos [?]: 772 [0], given: 33

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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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