In the figure above, is RS || PQ?

Question

quant_ds_00000066.jpg In the figure above, is RS || PQ? (1) x=y ; r=s (2) x=r ; y=s

mikemcgarry · Accepted Answer

Dear Awli I'm happy to respond. :-)

This is a great problem for visualization. For the relevant geometry, see: https://magoosh.com/gmat/2013/angles-and ... -the-gmat/ In a way, everything depends on that middle line, which I will call AB. Statement #1 : This statement has a kind of symmetry to it, and seems as if it would guarantee something, but look at a real case. statement 1 diagram.JPG RS isn't even pretending to be parallel to PQ. This arrangement of angles doesn't necessarily guarantee anything. This statement, alone and by itself, is not sufficient . Statement #2 : By contrast, this is classic statement of geometry. Technically, the angles set equal here are known as "alternate interior angles," and when these are equal, the lines absolutely have to be parallel. Here's a diagram. statement 2 diagram.JPG Because x = r = 40, it guarantees that AB is parallel to PQ. Because s= y = 60, it guarantees that AB is parallel to RS. Well, two things parallel to the same thing must be parallel to each other, so RS is parallel to PQ. This statement, by itself, provides sufficient information. First is not sufficient, second is sufficient. OA = (B) Part of what is confusing about statement #2 is that it does not guarantee that the oblique lines, AD and RB, are also parallel. You see, the diagram at the top suggests two sets of parallel lines, and we would need to know that all four angles are equal in order for both pairs of lines to be parallel. That would require the combined statements, but that is above and beyond what the question is asking. Does all this make sense? Mike :-)

Awli · Answer

For sure it makes sense. Thank you very much for your explanation. I've found it very useful and very clear.

Lucky2783 · Answer

Option B is sufficient . 
x=r middle line is parellel to bottom most line PQ.
y=s middle line is parallel to top one RS.