Data Sufficiency

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 of 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.



OA D

Lets assume,
Division X has = X full-time employees & x part-time employees
Division Y has = Y full-time employees & y part-time employees

Question is asking if X/x > (X+x)/(Y+y)

Stmt 1: Y/y < (X+Y)/(x+y)
==> xY+yY < yX+ yY
==> xY < yX
==> Y/y < X/x
I am not sure how to intrepret this inequality :roll:

Stmt 2: X > (X+Y)/2 & Y > (x+y)/2

Man...I give up ... I am yawning & this question is making it worse for me....time to go to bed

lets have 4 sets

XP, XF
YP , YF P= pt time, F=fl time

q is asking

XF/XP > (XF+YF)/(XP+YP)

simplifying q is asking

XF/XP > YF/YP ( cross multiplying and canceeling equal terms)
( when cross multiplying no term can be taken negative even in recession-struck market )
stmt 1 when solved yield the same suff

stmt 2 says YP> XP
XF>YF

hence automatically XF/XP > YF/YP suff

Hence D

dear sanju,

is that right approach. Please enlighten.

You are perfect Mr Misfit. Let me sing in the same timbre:

Xf/Yf is the full time in division X/Y, and Xp/Yp is part time in division X/Y, X, Y, and Z are number of employees in X, Y, and Z.

X = Xf + Xp

Y = Yf + Yp

Z = X + Y

For (1), Yf/Yp < Zf/Zp, as a reparation, Xf/Xp should be greater than Zf/Zp. Sufficient.

For (2), More than ½ of Zf /less than ½ of the Zp should be greater than Zf/Zp. Sufficient.

My explanation has shared thoughts of an unknown zone.