In general, collisions which involve things sticking to one another are not considered elastic.
Grant has the answer, though I'd neglect the bullet's contribution to moment of inertia, as 15 kg >> 1 g. The bullet has angular momentum about the hinge axis at the time of impact. (And before, but you don't care about that.)
Regarding the missing distance, it's no surprise that your textbook forget to mention exactly where the bullet hit. Just write "assuming the bullet hits the edge of the door..." in front of your answer.