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Each employee of Company Z is an employee of either division [#permalink]
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01 Aug 2005, 13:43
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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 parttime employees, is the ratio of fulltime employees to the number of parttime 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 fulltime 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
Joined: 04 May 2005
Posts: 279
Location: CA, USA

D
X for number of full time in X
Y ......... in Y
Z ......... in Z
Pz for all parttimer of Z
Px for all parttimer of X
Py for all parttimer of Y
Pz = Px + Py
from 1) => Pz/(X+Y)  Py/Y > 0
=> Pz*Y  Py*(X+Y) = Pz*Y (PzPx)(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



Manager
Joined: 13 Oct 2004
Posts: 236

OA is D.
Lots of calculations. Any one know of a simpler way to get to the answer?.










