The OP says his friend was interviewing for "product manager", which is not that. Product management is basically coming up with ideas for new products and seeing them through to the end. That includes helping design the actual computer program, which is why they ask software engineering questions.
(There are a ton of jobs called "PM", but they're all very different. None of them manage engineers, though, that's just "Manager" or "TLM".)
Working in this industry is just distressing. There are so many really clever people in this industry that cannot reason in any practical way (absolutely not calling you out, bubbleRefuge!!!) I work with a team that cannot figure source control out. People ask interview questions which a seconds introspection reveals will not measure real world performance. It goes on and on.
Sorry. I think I just realized I need a vacation. I deleted a much longer string of absurdities at the end of the paragraph above. My non-ranty point is that clever!=smart, and clever != job performance. Google has admitted in the press that their recommendations from interviews perform no better than chance. I don't get why that was hard to forsee. If you aren't measuring what you are trying to assess, chances are your results will be noise. "I wonder if this person is creative and can think up new product ideas. How will I determine that? Think, Roger, think. I know, I guess I'll ask him the math behind Cauchy distributions, and follow up with a problem in Hilbert space. That makes sense!" ;)
I upvoted you because it's not fair to down-vote people who are on topic, but you're not correct when you assume that of all things calculus (!?) should have anything to do with hiring a PM.
I honestly fail to see how solving some Cauchy sequence-related stuff 10+ years after you finished your studies has anything to do with managing a bunch of programmers. And I'm not saying this as an I-hate-maths guy, in fact the only A+ I got in college was in calculus, but were I to be given such a question during an interview I would have just left.