I have received a PhD offer from University A, but I'm also considering other programmes (say C and D), for which I will interview soon. 

I was wondering: should I mention during my interviews with C and D that I received an offer from A? What effect would this information have on my interview? Positive ("university A accepted him, so he should be a strong candidate"), or negative?

And let's say the answer is that I should not mention it, what if they directly ask me which other programmes I am applying to?