Help - GMAT Prep Ques 4 - See screenshot

[charu_mahajan]

Kindly help solve.

[GMATGuruNY]

Each employee of company Z is an employee of Division X or Division Y. 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.

This is a MIXTURE PROBLEM: Division X and Division Y are being combined to form Company Z.

If Division X and Division Y have the SAME ratio of full time to part time employees, then Company Z -- the MIXTURE of the two divisions -- will also have that ratio:
If X = 2:1 and Y = 2:1, then the ratio for Z = 2:1.

But if the two divisions have DIFFERENT ratios -- if the ratio for one division is GREATER than the ratio for the other -- then the ratio for Company Z will be BETWEEN the ratios for the two divisions:
If X = 4:1 and Y = 2:1, then the ratio for Z is between 4:1 and 2:1.

Thus, for Division X's ratio to be GREATER than Company Z's ratio, Division X will need to have the greatest of the three ratios:
Ratio for Division X > Ratio for Company Z > Ratio for Division Y.

Question rephrased: Is the ratio for Division X greater than the ratio for Division Y?

Statement 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.
Since the ratio for Division Y is LESS than the ratio for the MIXTURE (Company Z), the ratio for Division X must be GREATER than the ratio for the mixture (Company Z).
SUFFICIENT.

Statement 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.
Thus:
Division X = (more full time)/(less part time) = bigger/smaller.
Division Y = (less full time)/(more part time) = smaller/bigger.
Thus, the ratio for Division X is greater than the ratio for Division Y.
SUFFICIENT.

The correct answer is D.

[charu_mahajan]

Thank you very much.