请教一道prep数学

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.

请教第一个如何推出的？

设Fx，Fy分别表示X,Y部门的Fulltime人数，Px,Py分别表示X,Y部门的part time 人数，则问题问：(Fx+Fy)/(Px+Py)-Fx/Px是否小于0？

1）即(Fx+Fy)/(Px+Py)-Fy/Py>0

而(Fx+Fy)/(Px+Py)-Fy/Py=(FxPy-FyPx)/[(Px+Py)Py]（通分化简）,由1）>0，所以(FxPy-FyRx)>0(*)

问题中(Fx+Fy)/(Px+Py)-Fx/Px＝(FyPx-FxPy)/[(Px+Py)Px]（通分化简）,由1）得出(*)式(FxPy-FyRx)>0即（FyPx-FxPy）<0,所以(Fx+Fy)/(Px+Py)-Fx/Px<0

因此选A。