This will vary a bit by firm, so I'll speak primarily about McKinsey which was really the first firm to aggressively seek out non-MBA's.
The standard for analytical problem solving skills is the same for all entry level roles (undergrad candidates and grad school candidates) from all educational backgrounds. So is your thinking logical? The answers must be a "yes" regardless of your business or non-business background.
That being said, it is not expected that a JD or MD would know a lot of business terminology. So if you got the right idea, but you used the wrong term, that's okay. It won't be held against you.
It would help to have a general idea of how business works.
Companies sell stuff to customers. The money they make is called sales. What they pay employees and suppliers is called cost. A company is profitable if sales exceed costs.
Every market has suppliers and buyers... or supply and demand. It's better for a company if there is a lot of demand, and very little supply.
I'm being serious about this. You do need to know business at this common sense level, otherwise you won't be able to use common sense + logic to figure out the rest.
I suggest reading a few issues of Business Week or the Wall Street Journal to just get a feel for what topics come up a lot.