It is only limited by the interviewer's imagination in dreaming up scenarios. Write down the applicant's responses. Observe body language. Since there is no way a candidate can prepare for an HQ, you are getting a first hand look at how the individual thinks and acts under pressure. If written communication is important in the position to be filled, a variation is to ask for the response in writing on the spot and within a brief time frame.
Men are concerned with status and independence, women tend to negotiate and seek consensus.
A direct gaze from man to man may be interpreted as aggressive, from man to woman as too forward or possibly flirting. Women tend to look at each other when talking. They are looking to connect but it is not necessarily hostile or sexual. These and other aspects of male-female styles need to be considered and weighed for appropriateness by the interviewer, as do ethnic differences in communication. A good interviewer uses a method of communication involving support, collegiality, avoidance of one-upmanship, less lecturing, and more receptivity to the thoughts of the interviewee.