by **StaceyKoprince** Mon Jun 25, 2007 7:31 pm

Basically, you have to follow through a bunch of steps from one side of the triangle to the other. This is what I call a GMAT Proof problem - they use data sufficiency sometimes to write questions that seem somewhat proof-like.

So two of the angles are labeled 2x. That means the corresponding sides (BD and BC) are the same length. Draw little slashes on those lines to indicate they are congruent.

To the left of the middle 2x (by D), write 180-2x (because those two angles together add up to a straight line = 180). On the smaller of the two angles by letter B, write "y."

x + y + (180-2x) = 180 (because it's a triangle). The 180's cancel out and we have x + y - 2x = 0, or y-x = 0 or y = x. On your diagram, replace the angle labeled "y" with an x. **

Now, two angles in the smaller triangle are both labeled x, so the corresponding sides are also equal. Those sides are AD and BD. BD was also part of the earlier pair of congruent sides, so now we know that AD = BD = BC, and AD 6 (from statement 1). Sufficient.

** Slight shortcut here for next time. Know that the middle 2x is what's called an exterior angle of a triangle. An exterior angle is always equal to the sum of the two opposing interior angles (in this case, x and what we originally labeled y). In other words, we could have just said x + y = 2x, therefore x = y. But I wanted to show you the long way first to make sure you understood the actual proof behind it.

Stacey Koprince

Instructor

Director of Online Community

ManhattanGMAT