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Each employee of Company Z is an employee of either division

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Manager
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Each employee of Company Z is an employee of either division [#permalink] New post 01 Aug 2005, 12:43
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Each employee of Company Z is an employee of either division X or Division Y, but not both. If each division has some part-time employees, is the ratio of full-time employees to the number of part-time employees greater for Divsion X than for Company Z?

1 - The ratio of the number of full time employees to the number of part time employees is less for Division Y than for Company Z.

2- More than half of the full-time employees of Company Z are employees of Divsion X, and more than half of the part time employees of Company Z are employees of Divsion Y.
Senior Manager
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 [#permalink] New post 01 Aug 2005, 19:25
D

X for number of full time in X
Y ......... in Y
Z ......... in Z

Pz for all part-timer of Z
Px for all part-timer of X
Py for all part-timer of Y

Pz = Px + Py

from 1) => Pz/(X+Y) - Py/Y > 0
=> Pz*Y - Py*(X+Y) = Pz*Y -(Pz-Px)(X+Y) = -Pz*X + Px*(X+Y) > 0

to find if Px/X - Pz/(X+Y) > 0, we only need to find out if Px*(X+Y) - Pz*X > 0
we know this is true


from 2) => X+Y <2X and 2Px < Px+Py

therefore, (Px+Py)/(X+Y) > (Px+Py)/2x > 2Px/2X

that is: Pz/Z > Px/X
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 [#permalink] New post 03 Aug 2005, 06:36
OA is D.

Lots of calculations. Any one know of a simpler way to get to the answer?.
  [#permalink] 03 Aug 2005, 06:36
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Each employee of Company Z is an employee of either division

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