One Prep Quantitative Question

nazareth

How to resolve it? Many Thanks!

Prep #64. 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 the number of full-time employees to the number of part-time employees greater for Division 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 the full-time employees of Company Z are employees of Division X, and more than half of the part-time employees of Company Z are employees of Division Y.

Key: D

mymengming

PX   PY      FX    FY

FX/PX>FY/PY？

（1）FY/PY<(FY+FX)/(PY+PX)

化简即得

(2)(FX+FY)/2<FX

(PX+PY)/2<Y

化简后交叉相除即得

nazareth

Great explanation! Thanks a lot.

追梦人75

原文不是问的：FX/PX > (FX+FY)/(PX+PY) 吗？

kelu2008

Correct answer is :

Fz = FTE of company Z
Pz = PTE of company Z

Fx = FTE of company X
Py = PTE of company X

Fy = FTE of company Y
Py = PTE of company Y

Fz = Fx + Fy ..................(I)
Pz = Px + Py ..................(II)

Rephrased question: IS , Fx / Px > Fz / Pz ??

From Statement (1) :

Fz / Pz > Fy / Py

=> Fz.Py > Fy.Pz

=> Fz.Py - Fy.Pz > 0 .....................(III)

And also, ( Fx + Fy ) / ( Px + Py ) = Fz / Pz ....using (I) and (II)

=> Fx.Pz + Fy.Pz = Px.Fz + Py.Fz

=> Fz.Py - Fy.Pz = Fx.Pz - Px.Fz

=> Fx.Pz - Fz.Px > 0 [ using equation (III) ]

=> Fx.Pz > Fz.Px

=> Fx / Px > Fz/ Pz

Answer to rephrased question, YES

Hence, SUFFICIENT

From Statement (2):

Fx > Fz/2 and Py > Pz/2

But, Py = Pz - Px

so, ( Pz - Px ) > Pz/2

=> Px < Pz/2

As, Fx > Fz/2 and Px < Pz/2 , implies Px / Px > Fz / Pz

Answer to rephrased question, YES

Hence, SUFFICIENT

Choice (D)