For instance, they may ask: "What are your thoughts on the interview process so far?"
But chances are, they aren't craving your feedback. They aren't eager to know if they're doing a great job, or how they might improve for next time. No. They are trying to figure out how diplomatic you are.
James Reed, author of "Why You?: 101 Interview Questions You'll Never Fear Again," and chairman of Reed, a top job site in the UK and Europe, says in his book that the real question here is "How are your diplomacy skills?" - and that when answering it, he says, "You have to walk the line between flattery and criticism."
"At first glance this is a truly weird question," he writes. "Your answer couldn't be in any way relevant to the job at hand, could it? But maybe in a sort of sneaky way, it could."
He continues:
"While your ability to critique your interviewer is highly unlikely to be an essential skill should you get the job, the ability to offer constructive feedback while maintaining pleasant relations with colleagues almost certainly will come in handy. In all likelihood that's the essential political skill your interviewer is trying to test here."
A best way to answer this, he says, is by being truthful and constructive, while also showing respect for the interviewer. Reed suggests you avoid "pointless and obvious flattery," that you remain calm, and maintain your poise, while "channelling your inner diplomat."
Reed offered the following as an example of a great response:
"Well, I enjoyed the fact that we started off with a little tour of the facility on the way to the conference room and I definitely think you've done a great job of examining my job-specific skills. I really had to dig deep and think carefully when you quizzed me on how I'd handle the quality control issues you've been facing, which pushed me to get into the nitty-gritty of how I work and also have me a better idea of the challenges I'd be facing should I be offered the job. I don't think we've discussed my work style and the culture of the team I'd be joining as much, however. I'd love to get into how the team interacts and how I'd fit in. Is that something we'll be talking about later in the interview process?"