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 Div 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 Div Y than for Company Z.
(2) More than half of the full-time employees of Company Z are employees of Div X, and more than half of the part-time employees of Company Z are employees of Div Y

OA is D. Someone please explain. Thank you!

(1)
remember that ratios are the same as fractions in this sort of context.
this statement means that the FT employees are a smaller fraction of division Y than of the company as a whole. this means that they must be a bigger fraction of division X than of the company as a whole, because the fraction of the whole company that's employed FT must be between the two divisions' fractions.
sufficient.

(analogy: if i mix two powders together to make a shake that's 5% fat, and the first powder is 3% fat, then the second powder must be more than 5% fat)

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(2)
the first part means that (FT in div. X) > (FT in div. Y), and the second part means that (PT in div. X) < (PT in div. Y).
therefore, considering the ratio of FT : PT for each division, we have that FT/PT for div. X must be greater than FT/PT for div. Y. (this is the case because of either the numerator or the denominator: the numerator of X is greater, and the denominator is smaller.)
since the FT/PT fraction is bigger for div. X than for div. Y, it must be bigger for div. X than for the company as a whole (see the reasoning above under statement (1) for why this is true).
sufficient.

I think I was overwhelmed during the exam with the length of the question. After seeing your explanation I don't understand why I couldn't solve it.
Many thanks!!!

I'm not able to clearly understand this part. Could you please explain with a much more elaborate example.

1/
for us to help you, you'll have to specify what you didn't understand.

2/
what do you mean by “much more elaborate”?
i'll assume you don't actually mean elaborate, because an example that's actually elaborate, by definition, will be harder to understand than an example that's simple.

pick number to do this fast

100=30-fx+10-fy+20-px+40-py

30= number full time of x division.

finish in 1 minutes.

whoa, that doesn't work. you can't pick ONE VALUE for a data sufficiency problem, and then think you're done!
if you do that, you'll think that every statement is always sufficient.

it is possible to use number plugging on data sufficiency, but you have to plug in MULTIPLE possible values.
if you keep getting the same answer with all of your plug-ins, then the statement is sufficient.
if two of your different plug-ins give two different answers -- clearly something that can never happen with one plug-in -- then the statement is insufficient.