eBay Project Manager interview questions

I got first a quick phone screen with the University recruiter person, then I got an email to interview on site at the San Jose headquarters. The interview process on site lasted around 2 1/2 hours and it was very interesting. People there were very nice. I interviewed with around 10 more candidates. I had two different interviews with two Product Managers, and each one lasted around 45 minutes.

Got an interview at the campus recruiting event. Passed the interview. Then talked to the HR on a phone call. Then passed a skype interview with a product manager, and finally failed at the second Skype interview with a senior product manager. No behaviorals, surprisingly. The first Skype interview asked about resume and basic pm questions. The second Skype interview was intense on PM questions, like what do you think of this eBay product, why was it designed that way, how would you improve it. Also got asked if I know any machine learning algorithm.