Those are very much problem solving questions to test how you think, but I believe the more important point is that you don't freeze up and say, "Umm, I don't know." Even if you are wrong, keep thinking and talking about what you would do or what would happen. If you can think on your feet and react immediately, that is a very desirable trait in many places.
I work for the state, and I was on an interview panel in November. These are some of what I consider to be cultural questions.
"Tell me about a time when you had a major disagreement with your supervisor over a decision or policy."
The wrong answer is "I do what I'm told", and we all but got that from a couple of candidates. Be positive, speak up and talk to your supervisor, offer alternatives rather than just gripe, and ultimately comply with the decision of the supervisor. That's usually the right answer as the state doesn't want automatons.
"We have all worked with 'interesting' people. Tell me about a time when you worked with someone who was 'interesting'."
The questioner put emphasized the word 'interesting'. This one is tricky. Don't talk about the woman who raised goats. The right answer is to talk about someone who is difficult, weird, or both. Make it positive and talk about how you found alternative means to work with them or reach them, or reach them when others would not or did not. Especially in IT where I work, there are some very odd ducks. Because it's a vague question, it is a leading question that can draw people out and they end up volunteering a lot.