Hi,
From(1):
Let the no. of full-time and part-time employees of Division X be a and b respectively
Let the no. of full-time and part-time employees of Division Y be c and d respectively
c/d < (a+c)/(b+d) => (bc+cd-ad-cd)/d.(b+d) < 0 => bc-ad/d.(b+d)<0 => bc -ad <0 =>bc<ad
Adding ab on both sides we get bc+ab < ad+ab =>b(a+c) < a(b+d) => b(a+c)/b.(b+d) < a.(b+d)/b.(b+d)
=>(a+c)/(b+d) < a/b
So, the ratio of the number of full-time employees to number of part-time employees is greater for Division X than for Company Z
Sufficient

From(2): a > (a+c)/2 and d > (b+d/2) => 2a>a+c and 2d > b+d => a>c and d>b. So, ad > bc.
From this, we can proceed in the way we did for case(1)
Sufficient

Hence, the answer is D. As of now, I can't give a simpler solution. I will try to make it simple and post it if at all I get any.

Cheers!