Google Project Manager interview questions

A couple weeks after submitting through the site (with friend referrals), I got an email asking for additional info and to schedule a phone interview. That happened about a week later and turned out to be the most challenging interview of them all. I then had my onsite interview about 2 weeks later with 3 interviews with PMs in the morning -- much less of the brain-teaser / product case questioning than I expected -- followed by lunch with a PM. That's supposed to be off the record but I don't think it is. I think there's a threshold they look for in the morning which can result in 2 more interviews in the afternoon, 1 PM, 1 Engineer

Sent in my resume through a friend and was contacted by a recruiter by email a couple of days later. I never spoke with the initial recruiter. She set up a phone screen with a product manager for 10 days in the future. The first phone screen was rescheduled the day before it was scheduled to happen because the interviewer had an emergency, and was moved to a later date with a different interviewer the same week. The phone screen consisted of two major questions: one involving estimation (total storage required for all Gmail accounts) and customer retention (steps you would take to retain customers for a SaaS product). A week later the recruiter invited me to their office for a full-day onsite interview, which was scheduled for 2 weeks in the future. I spoke with 5 people on the day: 3 product managers, 1 product manager turned engineer (for the technical interview), and the Director of Product Management. Lots of estimation and design questions for the most part. The director was the only one who asked about my background. All interviewers were polite and seemed to answer my questions honestly. None of the questions I was asked were particularly difficult. A week later the recruiter called me to say that they didn't think my background was strong enough.