Data Sufficiency

You certainly can factor here, and it's a very good idea to do so. If you can get the factorization logitech arrived at, then the question is quite quick to answer. What you absolutely *cannot* do is divide both sides of your inequality by, say, (x-y). You need to know if (x-y) is positive or negative; if you don't know whether (x-y) is negative, you don't know if you need to reverse the inequality after you divide by (x-y).

This is the most common trap in GMAT inequalities questions: you will often see slightly complicated inequalities with unknowns, often with fractions, where you are tempted to multiply or divide both sides by an *unknown* (like x, or y, or as above, x-y). To do this, you need to know if the unknown is positive or negative. There are three good questions testing precisely this among the last 20 DS questions in the OG if you want more examples- I don't have the book at hand, but it's easy to pick out the inequality questions with letters and fractions in them.