Quadrilateral ABCD

by **NOV1907** Mon Oct 22, 2007 6:16 pm

Source (GMAT Sets 21-30: Set 21)

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by **RonPurewal** Wed Oct 24, 2007 5:23 am

OK, so I gather from your writing that you've already established the insufficiency of each of the individual answer choices. So let's just look at them together.

* Forget the letters in the second statement, which are only there to annoy you. The sole purpose of this statement is to say that 'two of the angles in the quadrilateral are X and 2X degrees.'
* Let's assume that two of the angles are 90.
- It's possible that the remaining two angles are X and 2X, which would make them 60 and 120 (there are 360 degrees in a quadrilateral).
- It's also possible that one of the 90 degree angles is 2X and that one of the 'other' angles is 45 degrees (and therefore the last angle is 135, although we don't really care).

These two points are enough to show that the answer is E. Incidentally, it's impossible for one of the 90 degree angles to be 'X' instead of '2X' (play with the numbers yourself to see why), although we've already settled the problem without thinking about that particular issue.

by **Nov1907** Wed Oct 24, 2007 11:57 am

Thanks Ron! I did consider that 90 was x. I did not consider the possibility that it could be 2x however. Thanks! I thought the letters were given to indicate that the angles x and 2x were adjacent to each other. Of course the solution doesnt change. Thanks again.

by **Guest** Fri Nov 02, 2007 11:06 am

Am I wrong to think that a quadilateral with 2 90 degree angles is always a square or rectangle?

by **StaceyKoprince** Tue Nov 06, 2007 12:48 pm

Sketch it and see if you can come up with something else. :) Don't forget to try putting the 90 degree angles next to each other AND across the diagonal from each other...

by **Nov1907** Tue Nov 06, 2007 8:28 pm

Something that I used to imagine quadrilaterals with 2 90 degree angles not adjacent to each other are cyclic quads. Think of a circle+diameter and two arbitrary triangles drawn on either side.