gmatprep geometry ds

From the question stem (the diagram), we know that BD = BC (sides opposite to equal angles)

Also, angle BDC = 2x = x + angle ABD (BDC is the exterior angle so it is equal to the sum of the 2 opposite interior angles)

Stmt1: AD = 6.
From our analysis of the question stem, we can evaluate ABD = 2x - x = x degrees. This means triangle ABD is isoceles. AD = 6 = BD.
We know BD = BC. Hence BC = 6.
Sufficient.

Stmt2: x = 36. We can calculate the value for 2x but this does not help calculate the length of BC. Insufficient.

Stmt1 is sufficient. Answer A.

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