"When applying for a position as a director, be prepared to have your leadership skills and judgement tested by many case studies. These scenarios help employers understand what kind of leader you will be for a team or department at their company, so confidence, quick thinking, and examples of how you have fixed similar problems in the past will be highly advantageous towards receiving an offer."
I didn't find any question particularly difficult or unexpected. If forced to chose one it was when she asked how I would react to C-level executive/s shooting down a concept I developed for a seasonal campaign.
I explained that I would be okay with that. That said, I also explained I am diligent and if I felt very strongly that the direction I was offering was paramount for the direction/growth/evolution of the brand, I would fight for it.