I believe the hoop stress vs. longitudinal stress question is approximately true specifically for thin-walled pressure vessels. However, it is many many years since I would have been able to prove that--probably about the time I took the final exam in that particular course :-)

Especially given modern computer tools, I'm actually not sure how many mechanical engineers would be able to derive that sort of thing in an interview. I wouldn't have been able to but you probably didn't want me designing rockets either.