Google Product Manager interview questions

Friend submitted my resume. Recruiter got in touch to set up a phone interview after a day. Had the first interview a couple weeks later. Had to ask for an update before I knew they wanted me to go through another phone interview a week after the first one. Had a second phone interview. Waited about 10 days, then reached out for feedback. Recruiter called me right away to let me know we were not moving forward. Recruiter explained that in their experience, Product Mangers with a lot of business savvy, but without a technology background (which was very clearly not in my resume) don't last very long (more than two years) at Google. Her explanation for thinking I might be a good fit originally was with the hope that I had self-taught some technical/computer science skills. ...This all flies in the face of having asked this question of the first interviewer whose response was, "We don't need engineers for this role. Use what you're good at." The second interviewer was a computer science guy turned product person and arrogantly asked, "How do you expect to work with the top 1% of computer science engineers in the WORLD without any computer science background?" Left a very bad taste in my mouth. The recruiter thought I would be a good fit in other roles at Google and asked me to let her know what else I was interested in. I won't be applying again. Yet another talented woman filtered out of Google.