Is there a pattern or trend of what kind of case problems are given by a particular firm ? For eg: BCG generally gives M&A cases while Mckinsey generally gives business cases ?
The cases you get are all over the place and there's no pattern that I've ever seen or heard about. The one pattern that DOES exist is that 50% - 70% of the time, the case comes from that particular consultant's personal work history at the firm.
So if your interviewer works with insurance companies, there's a good chance you'll get an insurance case. If they work in high-tech, you'll get a high tech one, etc...
Cases can also vary by geographic location of the office. For example, McKinsey Houston I've heard has a lot more Oil & Gas cases than say McKinsey New York City - which has more finance, media, and retail.
The reason for this is the good cases (from an interviewer's stand point) has REAL data gathered by REAL consultants. So when you ask for X data (and assuming that's the proper thing to ask for as the next step in the case), very likely the person interviewing you personally asked the client for X data several weeks/months ago.
You know you nail such a case when you basically retrace the consultant's entire analytical process from start to finish... asking the same question they asked on the job in the real world, looking for the same data they looked for previously, and coming to the same conclusions they did (based upon looking at the same data).
Also some times it seems like the interviewer's are out to get you... but it is far from the reality. All interviewers are also consultants. Their main job is to work with clients... and they do interviewing as a side project. Up until perhaps the hour or day before your interviews start, many aren't even thinking about what cases to give.
I've run into colleagues in the lunch room who were off to give a case interview. One person asked what case should I give my interviewees? I looked at a bottle of water on the lunch table and said, why not give a case on bottle water - you know a market entry case for a soft drink company... I hear water sales have been growing. So the other person said, hey that's interesting and off she went to interview someone.
I've made up cases in the elevator on the way to going to the right floor to meet my candidates.
So amongst the interviewers, the case interview is pretty casual... most favor basing the case on some actual client project (name changed of course) mostly because it's no prep work as all the data is in the interviewer's head.
Other times we'll just make up a case, have a specific client problem in mind, and then make up the data that would lead to isolating that particular problem (e.g., industry pricing has been slashed due to overcapacity... but this problem first presents itself as the client is losing money and wants you to help).