请教GPREP 的一道数学题

missdandan

Each employee of Company Z is an employee of either division X or division Y, but not both. If each division has some full-time emplyees and some part-time employees, is the ratio of the number of full-time employees to the ratio of the part-time employees greater for division X than for company Z ?

(1):The ratio of full time employees to part-time employees is less for division Y than for company Z.

(2): More than half of the full-time employees for compnay Z are in division X, and more than half of the part-time employees for company Z are in division Y.

读完题目就已经晕菜了。。。，最头疼的就是这类题，请大家介绍一下对这类题有没有好的解题方法？谢谢！

missdandan

thanks  a  lot !!!

Economics

Let's denote Fx as the number of full time employees in division x, Fy as the number of full time employees in division y, Fz as the number of full time employees in company z. Because x and y are the only two divisions in company z, so Fx + Fy = Fz.

Similarly, we denote Px, Py and Pz as the numbers of part time employees in division x, division y and company z, respectively. Again, Px + Py = Pz.

Condition (1) says: Fy/Py < Fz/Pz = (Fx+Fy)/(Px+Py). This can be rewritten as Fy*(Px+Py) < (Fx+Fy)*Py, or further, Fy*Px < Fx*Py, or Fy/Py < Fx/Px. The conclusion is that the ratio of full time employees to part time employees for division y is less than for division x.

Condition (2) says: Fx > Fy, Px < Py. So Fx+Fy <2Fx, Px+Py>2Px, then Fz/Pz = (Fx+Fy)/(Px+Py) <2Fx/2Px = Fx/Px. It can be determined that the ratio of full time employees to part time employees is greater for division x than for company z.

So B is the answer.