In the figure below, l1 and l2 intersect l3. Do l1 and l2 intersect to

Sure, helipatel91198. I would start by pointing out that you should not let your eyes deceive you, especially when it comes to DS questions, in which assumptions can get you into trouble quickly. I know that the two lines look as though they will converge to the right of line 3, but we cannot let this apparent truth cloud our reasoning. We can only take what the question stem and statements provide as factual information.

Looking at Statement (1), we can picture a skewed bird's-eye view of three streets, in which lines 1 and 3 intersect at a 90 degree angle. If this were true, then y would be 90, and x could be anything greater than 90, even 91. We know that if x and y are both right angles, the two lines will be parallel, right? Well, if x + y > 180, it must be true that lines 1 and 2 would converge to the left of line 3, and if x + y < 180, they would converge to the right (just the way they look in the image above). To illustrate, with line 3 removed, use familiar mathematical symbols:

x + y > 180 → < (will open to the right, converge on the left)
x + y < 180 → > (will open to the left, converge on the right)

Again, I know the image makes it look as though the bottom inequality is at work, but based on the statement alone, we have no way to tell what the sum of the two unknowns would be, relative to 180 degrees. Thus, Statement (1) is NOT sufficient.

Since Statement (2) tells us directly that the sum in question is less than 180, we can be certain that our eyes are not deceiving us, and that the lines will intersect to the right of line 3. Thus, Statement (2) is sufficient, and the answer is (B).

Bonus: This question reminds me of a difficult PS question from GMAT Prep. I am attaching the image of the question below for discussion, but I will not spoil the actual question. Feel free to head over to that other thread if you want to work through the problem and read the community dialogue.

A word of advice: watch out for assumptions.

Good luck with your studies.

- Andrew