请教一道题

3．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 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.

看到大家有如下解释：设x部门的fulltime人数是fx,parttime人数是px,同样y部门的是fy和py.

那么我们要比较的就是fx/px与(fx+fy)/(px+py)之间的大小.

条件(1)能推得fy/py<(fx+fy)/(px+py),可以这么想:有一个分数m/n,当分子分母都增加了一点(如a和b)后,值变小了.,那么a/b和最终的结果之间谁大?回答是不知道.(要证明的话可以从曲面z=x/y中得出,好象叫双曲面吧,不记得了.).

条件(2)能推得fx>fy且px<py,这时思路跟刚才差不多:一个分数fx/px,当分子增加fy后,分子fx+fy<2fx,当分母增加py后,分母px+py>2px,所以(fx+fy)/(px+py)<fx/px

选D

想问一下，我们设定了X,Y分别为X,Y车间的人数，当X车间的full time = xf 时候，我们如何能确定Y 车间的full time和Y车间的总人数的比例仍是f ，即与X车间比例相同呢？

请指点。