1. the ratio of number of full time employees to number of part time is less for division Y then for company Z

=> Ratio of full time to half time employees for company Z should be median of the ratio for division X & Y. And since ratio for division Y is less, ratio for division X must be grater then the median i.e. must be grater then the ration of company Z.

Statement 1 alone can answer the question

2. More than half of full time employees of company Z are in X and more than half of part time are in division Y

=>As per the given condition let's consider the worst case,

let say company Z has A full time and B half time employees. Now as per given condition division X will have (A/2) + 1 full time and (B/2 - 1) half time employees in worst case scenario.

Thus ratio for division X = (A+2)/(B-2)
And ration for company Z = A/B

Clearly (A+2)/(B-2) > A/B....( since number of employee can't be negative.. :!: :!: )

Statement 2 alone can answer the question.

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Please correct me if I am wrong anywhere....

OA is (d)..

thanks umang...

(1) is easily sufficient because the ratio of full:part for the company will be somewhere between the ratios in the Divisions. Since the ratio for Y is less than for the ratio of the whole company, the ratio for X must be greater than the ratio for the whole company. SUFFICIENT.

(2) If we call p the number of part timers company wide and f the number of full timers. we know that division X has more than .5f but less than .5p. So ratio of full time to part time is something like .6f/.4p for division X, but .4f/.6p for division Y. We can be sure that the ratio is higher for division X. SUFFICIENT

The answer is D

A more elaborate algebraic solution as well as a step by step video solution is available at GMATPrep Question 1028. To practice similar questions, set topic='FDPs & Ratios' and difficulty='700+' in the Drill Engine.

Good luck,
-Patrick

PS. This question is also discussed at https://www.beatthegmat.com/company-z-di ... 42389.html and https://www.beatthegmat.com/very-hard-fu ... 61763.html