Because it's an EOC, I don't think it goes on my PRD. However, when I interview for an airline, I believe I'll have to disclose it. I won't say anything bad about the school, I'll just say that the experience taught me the importance of studying harder and not doubting myself.
Regarding the question, my instructor told me that any airline interview committee will likely laugh at the fact that I was failed over that one question (since he thought it seemed so petty).