Proportions - Can someone help me find a solution

[geet_ge]

Each employee of company Z is an employee of either Division X or 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 Y?

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


1) A alone
2) B alone
3) Both
4) Either
5) Neither

[Anurag@Gurome]

Each employee of company Z is an employee of either Division X or 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 Y?

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


1) A alone
2) B alone
3) Both
4) Either
5) Neither

Let us assume number of full-time employees for division X = Xf
Number of part-time employees for division X = Xp
Number of full-time employees for division Y = Yf
Number of part-time employees for division Y = Yp

Then question is: Is Xf/Xp > (Xf + Yf)/(Xp + Yp)? or is XfXp + XfYp > XpXf + XpYf? or is XfYp > XpYf?

(1) (Xf + Yf)/(Xp + Yp) > Yf/Yp
XfYp + YfYp > XpYf + YpYf
XfYp > XpYf, which answers the required question; SUFFICIENT.

(2) (Xf + Yf)/2 < Xf and (Xp + Yp)/2 < Yp
Yf < Xf and Xp < Yp, which implies XpYf < XfYp, which again answers the required question; SUFFICIENT.

The correct answer is D.