varun289 wrote:Each employee of company Z is an employee of Division X or Division Y. 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.

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.