How can we know for sure that AD = DC or that AB=AC? This information is required for (1) to be sufficient and A to the correct answer.
If we look at the diagram they look equal but their is no proof in the information...
DO we assume in the GMAT that if the lines look equal they are equal? I always though this was a 'no no'
Area of a triangle = 1/2 * base * height, and here the base is AC, while the height is BD.
Statement 1 tells us the product of the base and height, i.e. BD*AC = 20.
Since the question is asking about the area, we know that the area is 1/2 the product of BD and AC.
With this statement, we do NOT know for sure that AD = DC / AB = AC / the lines are equal... frankly we don't need to know for this statement to be sufficient. We have the product of BD and AC, and given that the area is half of the product, we have enough information to answer the question.
Statement 2 (that angle BAC, x, is 45 degrees) implies that ABC is isoceles (AB=BC), but this is NOT enough to give us any idea (on its own) about AC or BD. Hence this statement is insufficient and A is the answer.
Hope this helps.