I have been to a couple of interviews (BCG, McKinsey etc.), and during a few of these interviews I feel that I am not given the possibility to come up with a structure. It will go down something like this: Regular case presentation (e.g. cost reduction for train company), and then without stopping (and giving me the opportunity to ask clarifying questions, objectives and come up with a structure) the interviewer asks a brainstorming question.
Typically, I hesitate a little, ask the most important clarifying questions, ask for time to come up with ideas for the brainstorming and then present it. After that the interviewer typically wants to dig deeper into the different ideas I had, and we never get back to writing up a structure for the case.
How should I handle situations like this? Could it be that the brainstorming question indicates that we are only focusing on that particular issue that the brainstorming indicates (and that the structure for the brainstorming question in a way becomes the issue tree for the case)? Should I just go with the flow and forget the issue tree (like I've done)? Should I ask if the interviewer want me to draw up a structure for the case before I answer the brainstorming question?