Data Sufficiency

ANS:D

Im just baffled!!
wht is the source plz?

I got that question in GMATPREP exam

dear friend the answer would be D
Key : the average ratio for the company z will be the average of the ratio for both the divisions x & y i.e.
Avg. ratio of company Z = (ratio of div. X + ratio of div. Y)/2

let us look at 1)
The ratio for div. y is less than the avg. ratio which means the other division must have a higher ration than the average to make it balanced....which tells us that div. X will hav the higher ratio than company Z, so it is sufficient

and for 2)
s per the given condition let us assume,

Full time employees are divided as 0.6 in X and .4 in Y while
Part time employees are divided as 0.4 in X and .6 in Y, (here you can take any value for the division of employees but make sure you follow the rules of cond. 2 and you will always get the same relation between the ratios)

now ratio F/P for X = .6/.4 = 3/2
and for Y it is = .4/.6 = 2/3

so ratio for X > ratio for Y and as z is the avg of both, Y<Z<X which again proves that ratio of x is >ratio for Z which means 2 is sufficient

so the ANS is D

Note that the company ratio for the number of full-timers to part-timers must
be between the corresponding ratios for Divisions X and Y if these ratios are not
the same.
(1) As Division's Y's ratio is below the company average, Division X's ratio
must be above the company average. SUFF
(2) Division X has more than half of the full-timers and less than half on the
part-timers, and Division Y has less than half of the full-timers and more
than half of the part-timers. Thus division X's ratio will be greater than
division Y's and thus Company Z's. SUFF

With algebra:

Suppose that the company has f full time employees and p part time employees, and that division x has a full-timers and b part-timers. Note that division y has f - a full-time employees and p - b part-time employees

We want to know whether a/b > f/p i.e. whether ap >bf

(1) (f - a)/(p - b) < f/p i.e. p(f - a) < f(p - b) or -pa < -fb or pa > bf SUFF

(2) a > f/2 b < p/2 thus a/f > 1/2 and b/p < 1/2 so a/f > b/p and ap > bf SUFF