Google Product Manager interview questions

The interviews were by engineers on technical knowledge and basic programming skills (e.g. understanding recursion and iteration), as well as product managers who covered business models, strategy, approach to designing products, and a lot of mental modelling and calculation exercises, to see how a candidate breaks down a problem and figures out a rough answer - in one or two cases a precise numeric value was required, not just a description of the variables that would be used to calculate it.

I was contacted by a Google recruiter, and said that Google was interested in my background. He asked me to provide some additional information -- GPA for undergrad and grad school, GRE scores(!), etc. The recruiter communication was smooth, but I don't understand the emphasis on GPA and test scores for someone with over 12 years of work experience. Anyway, I was scheduled for a phone interview with a Google product manager for ten days later. The phone interview lasted 45-50 minutes, and was very conceptual, other than an initial "tell me about yourself" question). There were several hypothetical questions about products, and some questions about Google's market position and competitors. The interviewer was very methodical and polite, and even though I knew by the end of the interview that I had not satisfactorily answered all his questions, I left with a good feeling about the overall experience, because the questions were thought-provoking and open-ended, and I had fun answering them.