求教战友们一道PREP数学题

林清月

202.    19528-!-item-!-187;#058&012279
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.
此题选D...求教第二个选项怎么推出来的..
还有就是 有无简便的方法判断...拜谢！

chinamerica

Denote
fz (or fx, fy):  full-time employees of Company Z (or X,Y)
pz (or px, py):part-time employees of Company Z (or X,Y) .  

fz=fx+fy    pz=px+py
Is fx/px greater than  fz/pz?  
 
(2)   fx > 1/2 fz
       py> 1/2pz implies px< 1/2pz  (since pz=px+py)
thus fx/px > 1/2 fz/(1/2pz) = fz/pz

rzhong

fx>fy, px<py => fxpy>fypx

fx/px     fy/py

fy/px*py/fy=fxpy/pxfy
so, it's greater than 1

林清月

Denote
fz (or fx, fy):  full-time employees of Company Z (or X,Y)
pz (or px, py):part-time employees of Company Z (or X,Y) .  

fz=fx+fy    pz=px+py
Is fx/px greater than  fz/pz?  

(2)   fx > 1/2 fz
       py> 1/2pz implies px< 1/2pz  (since pz=px+py)
thus fx/px > 1/2 fz/(1/2pz) = fz/pz

-- by 会员 chinamerica (2010/10/6 3:40:44)

多谢多谢~

林清月

fx>fy, px<py => fxpy>fypx

fx/px     fy/py

fy/px*py/fy=fxpy/pxfy
so, it's greater than 1

-- by 会员 rzhong (2010/10/6 10:04:45)

many thx~