raj44 wrote:1. In an Isosceles Triangle ABC, point D lies on segment BC. Angle B is 40 degrees. What is the value of angle DAB?
1. AD is angular bisector of angle A.
2. AB x CD = AC x BD

E

Statement (1) Angle A could have a variety of measures. We only know that the triangle is isosceles. We don't know what that means for angle A or half of angle A.

Insufficient

Statement (2) This statement is interesting because it possibly indicates that sides AB an AC are equal in length. However, that's not a good trap to fall into because actually there are multiple ways to make AB x CD = AC x BD. For instance, the two sides, AB and AC, could be equal to each other and also CD and BD could be equal to each to each other. Alternatively, the two sides could be unequal in length with CD and BD also unequal in length.

Insufficient

With the statements combined, oh man I want to jump and say "Sufficient," thinking that if AD bisects angle A, then the only way AB x CD = AC x BD, would be if the AB = AC. Have to really consider this first though and I think I am going to go with while I am sure there is a way to answer this, it is beyond the scope of the GMAT. So I turned this image around a bunch of ways and got a good learning experience, and I am going to leave it at that for now.