Hi Clinton,
in the future, please post Data Sufficiency questions in the Data Sufficiency (not the Problem Solving) section so that we can try and keep things a bit organized!
Now, on to the question.
(2) is easier to evaluate, so we should look at it first. It gives us no information about length at all. Yet the question is asking for length, so (2) is easily dismissed as insufficient.
Why is (1) sufficient? First takeaway: in multi-figure problems, pass info from one shape to the next!
We know that a half-circle is always 180 degrees.
...therefore, angle ADB must be 180-2x. We also know that the angles of a triangle sum to 180 degrees.
...so, angle ABD must be 180 - ((x) + (180-2x)). Solving for angle ABD, we see that it must also be x.
Since sides BD and AD are opposite equal angles, they must be equal in length. So, side BD is 6. And, again, since sides BD and BC are opposite equal angles, side BC must also be 6.
[spoiler]So, (1) is sufficient by itself. (And (2) is not. The correct answer is (A)).[/spoiler]
Kaplan Teacher in Toronto
