Google PM interview questions

I applied through a Google Recruiter I met at one of the Google events for developers at their Mountain View campus. Initially, there was a some miscommunication where the recruiter assumed I was applying for a technical position when in fact I was looking for a product management position. Once that got cleared, I had a phone interview with a senior product management professional. Overall, this phone interview lasted about an hour.

First you work with a recruiter who decides whether to put you through to the next round. Next you have a phone interview, where a current Product Manager begins by asking several questions. Why Product Manager, why Google, etc. Then you are given several case questions. These questoins can be oddly specific and stump even the best efforts to prepare. No feedback is given.