GMAT Prep - Parallel Lines

here's a way of thinking about it if you don't know trigonometry.

statement (1)
since angle X is bigger than angle Y, it follows that segment PQ is steeper (i.e., has a greater slope) than segment RS.

imagine drawing perpendiculars (which in this diagram would be vertical lines) down from P and S, and considering the right triangles thereby formed.
the vertical legs of those right triangles would have the same length, because they're drawn between the same parallel lines.
the horizontal leg of the triangle with hypotenuse PQ would be shorter, though, because the slope (= rise/run) is greater. since "rise" is identical, as just mentioned, the fact that (rise/run) is greater means that "run" must be smaller.
because the vertical legs have the same length and the horizontal leg of the left-hand triangle is shorter, it follows that the left-hand hypotenuse (i.e., PQ) is shorter.
sufficient.

(2)
this statement is symmetric in x and y, meaning that you can switch x and y without consequence.
consider two cases in which this happens: say, x = 40 and y = 60, and then x = 60 and y = 40.
in the latter case, the reasoning is the same as for statement (1); in the former case, it's the opposite, and PQ is now longer.
insufficient.

answer = a

lunarpower wrote: (2)
consider two cases in which this happens: say, x = 40 and y = 60, and then x = 60 and y = 40.

I'm sure Ron meant- say x=40 and y=50 (not 60), and then, say x = 50 and y = 40 (since x+y = 90). The analysis is perfect otherwise. For statement 1), you could imagine the line segments PQ and SR to be ladders, and make it a real-world problem: of course, if y is smaller than x, then SR should be longer than PQ.