The first question you propose is the first question I ask in every interview that I conduct, and I can count on my fingers the number of people who have given

The first question you propose is the first question I ask in every interview that I conduct, and I can count on my fingers the number of people who have given me a satisfactory answer to this question. It really colors my perception of your skills - whether you lied on your resume, whether you were dead weight on your team while they did all of the work, whether you were clueful about what was going on where you were working before, and so on. The only time that I have recommended someone be hired who was not able to answer this question was when they were under an NDA and were not able to talk about the work they had done. That candidate aced the practical side of the interview that I gave ("Here's a scenario at a high level using the skills you claim to have, what would you do and why?") and is the best worker I have ever recommended to hire.