Tough Question

[ashforgmat]

Each employee of company Z is employed in 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 number of part-time employees greater for Division X than for Company Z?
a. Ratio of number of full time employees to part-time employees is less for division Y than for company Z
b. More than ½ of full-time employees of company Z are employees of div X, and more than ½ of part-time employees of company Z are employees of div Y


Hi People,

What will be the fastest way of solving the above problem?

[liferocks]

------FULL Time---Part Time---ratio
X----f1----------------p1----------f1/p1
Y--------f2------------p2----------f2/p2
Z-------f1+f2------p1+p2-------f1+f2/p1+p2

from 1
f2/p2<f1+f2/p1+p2
or f2p1+f2p2<f1p2+f2p2
or f2p1<f1p2
or f2p1+f1p1<f1p2+f1p1
or p1(f2+f1)<f1(p2+p1)
or f1+f2/p1+p2<f1/p1....the ratio of the number of full-time employees to number of part-time employees greater for Division X than for Company Z..sufficient

from 2

f1>f2..and p1<p2..hence f1/p1>f2/p2 or f1p2>f2p1..as the steps followed in condition 1 it can be shown that the ratio of the number of full-time employees to number of part-time employees greater for Division X than for Company Z..sufficient

Ans option D

[ashforgmat]

Thanks a lot for the gr8 reply...