Draw a perpendicular from point b onto the extended line segment DC. statement one tells us that this triangle formed is a 30-60-90. We r given the length of the hypotenuse 6 root 3.
Thus the base is 9. Also we get the new small right triangle with one perpendicular as 3 root 3(applying 30-60-90 formula to the larger triangle) and the base as 3. Thus this is another 30-60-90 and the length of its hypotenuse bc is 6.

Correct answer is A.

statement 2 is pretty bland without any relevant legnths given. We cant locate the location of point C correctly.

30-60-90 shortcut :

smaller side = 1/2 * hypotenuse
larger side = 1/2 * hypotenuse * root3

(2) works here easy. It is sufficient. I was having problems with (1).

kiton wrote:(2) works here easy. It is sufficient. I was having problems with (1).

did i solve ur problem; or I added something to it ?

First of all, thank you for your comment ( i was a bit busy and did not have a chance to write a proper reply).

Yes, you definitely have clarified the problem (statement 1) to me.

Secondly, please, notice, that the second statement is also sufficient. The OA is D.

wow this was tough, I think the second statement actually follows from reversing the calculation that I have shown.