Data Sufficiency

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 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 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.

naveen451 wrote: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 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 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.

tricky one

We can also try to approach this using logic rather than algebra:

In order for the ratio of FT:PT to be greater for X than for Z, it has to be greater for X than for Y, since Z is made up of X and Y.

Statement 1 says that the ratio of FT:PT is less for Y than for Z. The only way for this is possible is if the ratio of FT:PT is greater for X than for Z. Sufficient.

Statement 2 basically says that X has more than half of the FT and less than half of the PT. So,it has a relatively large ratio of FT:PT. On the other hand, Y has less than half of the FT and more than half of the PT. So, it has a relatively small ratio of FT:PT. So, the FT:PT ratio is larger in X. Sufficient.

I know that's a lot of words, but I encourage you think through the steps above and see if it's helpful for you, because if applied correctly it might save some time.

D