If x and y are positive. is y< 2 ? (1) x > 2y (2) x < y + 2

Neither statement is sufficient alone; from statement 1, we might have y=1 and x=10, or y=3 and x=10, and for statement 2 we might have y=1 and x=1, or y=5 and x=1.

Combining the statements, there are a few ways one could look at this question. You have the following two inequalities, rewriting the second one so both inequalities face in the same direction:

x > 2y
y + 2 > x

Recall that we can add two inequalities which face the same way, just as we add equations (be careful though - you cannot subtract inequalities in this way). Doing that here we have:

x + y + 2 > 2y + x
y + 2 > 2y
2 > y

so the answer is C.

Or, perhaps more simply, you could 'chain' the inequalities together. Here we know that x > 2y, and x < y+2, so we must have that

2y < x < y + 2

So certainly 2y < y + 2, or y < 2.

Most test takers find abstract inequalities questions difficult, so any similar question would be at least a medium-high level question. One takeaway here: if you see an inequalities problem that looks like a 2 equations/2 unknowns problem, and if you don't see anything else to do, then try lining up your inequalities and adding them to see what happens. Often that will give you the answer you're looking for, as it did here. Of course there are often more direct approaches, like the one I used in the second solution above, but if you don't see that kind of solution quickly, adding your inequalities might get you there.