Classic cases for consultants: you are presented with a client situation (usually a strategy case, with a scenario where the company is presented with a challenge and is seeking the help of McKinsey. Two options: grow the business or cut costs/downsize.
The consultant is expected to list the drivers that will the company to grow. It's useful and expected to structure the question really well, saying "I can think of x number of drivers. Let me list them and go into further details with each".
Important to think about the internal dynamics of the organization (financial resources, human resources, organization, etc.), but also the external factors, such as competition, regulatory environment, etc.
There is then a part with maths (simplified to be able to do it without a calculator) where the candidate is asked to calculate growth of a product/service, cost per unit, change over time, etc. Walk the interviewer through your reasoning so that he/she can stop you in case of a math mistake.
Wrap up: from what you know about the organization, the strategy questions raised at the beginning and the maths that you did, what do you recommend to the CEO of the "client" that has hired McKinsey? provide clear recommendations and argue your point (don't say that we would have to do more analysis, or that the client has several choices - remember you are going to advise some deciders to lead their business)