I was also able to solve only based on the hints given by them but not able to get those extended questions with correct intuition at that point of time. It's just that the right ideas didn't click at that moment.
I was asked to draw a budget line and then identify the optimal points when the alpha =1 ,<1 . First part I was correct but second I said it will be concave when it is convex ( risk averse), then because of time constraint , I was asked to point optimal points if the indifference is convex.