Company Z has part time and full time employees in both divisions X and Y (the only two divisions in the company). We want to know if the ratio of FT:PT is higher in X or in the company as a whole.
(1) FT:PT for div Y is < FT:PT for the whole company
FT:PT for the whole company will be a weighted average of the ratios for divisions X and Y. If the ratio for division Y is below that weighted average, then the ratio for division X must be above the weighted average (since the average of two groups is always somewhere between the groups).
Therefore, statement (1) gives us a definite "yes" answer: sufficient.
(2) More than 50% of the FTs work in X, more than 50% of the PTs work in Y.
If more than 50% of the FTs work in X, and fewer than 50% of the PTs work in X (since more than 50% of the PTs work in Y), then X has a relatively higher proportion of FT to PT than the entire company.
Therefore, statement (2) gives us a definite "yes" answer: sufficient.
Each statement is sufficient alone: choose (d).
