GMATPrep Question - Math_DS

Inituition says D here!

Let's see if I have the math to confirm it. Employees are either full time or part time. So we can simplify the question a little

If px, py and pz are the precentages of the employees of div. X, div. Y and Z that all full time, and nx, ny and nz the numbers of employees in X, Y and Z (nz=nx+ny) the question is equivalent to:

Is px > pz?

In general pz(nx+ny)=nypy+nxpx
ny(pz-py)+nxpz=nxpx

(1) says that pz-py > 0

So, nxpz<nxpx and pz<px SUFF

Really, when you think about it, it makes sense that either pz is between py and pz or px=py=pz ... (1) says py<pz , so it must be that pz<px

(2) Suppose pz ≥ px. Thus py ≥ pz and 1-px≥ 1-pz≥ 1-py

pxnx> 0.5nzpz So nx>0.5nz (a)

(1-py)ny>0.5(1-pz)nz. So ny>0.5nz (b)

Adding (a) and (b) we get, nx+ny>nz

However, as there is no overlap between divisions X and Y, this can't be true.

Thus px>pz SUFF


Answer D