Case interviews come in all formats. The key, as an interviewee, is being prepared. Know what the interviewer is looking for, know the industry/sector, the jargon, the constraints and stakeholders, and how people in the industry operate. Government and nonprofit cases span a wide variety of problems, issues, stakeholders, and politics, which makes them trickier than private sector case interviews.
Public sector and nonprofit-focused divisions have sprung up from elite consulting firms. These firms are looking for talented, intelligent, mission-oriented people with an understanding of the public sector and a desire to measure their results with an organization's mission rather than it's bottom line. Ask not... JFK
