How would you answer an interview scenario involving API versioning strategies?

In an interview, I would first define API versioning strategies and the problem it solves, then explain how I would version only when compatibility requires it, document support windows, keep behavior consistent within a version, test older clients, and provide a migration path. I would also call out the main failure mode: creating a new API version for every internal refactor quickly multiplies maintenance cost without giving clients meaningful contract stability. Finally, I would describe how I would test, monitor, and safely roll back or recover the solution.