I am a bit dismayed that the majority of answers here seem to take as a given that the OP is in some contest of wills with her fellow grad student and give advice for "winning the battle," "putting the other student in her place," "effecting her demise" and so forth. (Not all: there are some excellent answers and indeed some which are very close to what I am about to say: just too few of them in the total chorus.) This is fundamentally wrong-headed: graduate school is not a battle of wills with other graduate students. It does (unfortunately) have a competitive aspect, but the competition is not for top spots in the social/professional hierarchy of graduate students: it is for academic excellence and the opportunity to continue one's academic career.
How are these true goals of graduate school furthered by this verbal jousting with a fellow grad student? The answer is clear: they're not. Being the victor in a verbal joust feels better than being the loser, but the victory is completely pyrrhic. The only real victory is to stop playing this game.The only real victory is to stop playing this game.
The OP can do that as follows: she should think carefully about the range of interactions she has with her fellow student and make a clear, mental divide between activities which are necessary (they may have to work together, after all) and potentially productive and activities which are part of the no-winners game described above. Then, in all future interactions with this other student, she should simply refuse to engage with all overtures that she knows or strongly suspects will be unproductive. She should respond positively to interactions that are clearly productive/professional, and she should firmly move borderline interactions towards the productive/professional direction. All these things she should do completely openly and unsubtly. That there are other people around is a good thing for this strategy: the OP is saying "come to me with professional things and professional things only." To refuse to do that when other people are around makes the other person clearly in the wrong.
"I'm sorry, I've answered questions like that from you before, so I know it won't lead anywhere productive. Do you have anything constructive / relevant / about project X to ask me?"
The lack of subtlety of this strategy should make it straightforward to implement as long as the OP is committed to it. The worst possible outcome I see is that the OP is already so bent out of shape / her fellow student is evil enough that interactions that look innocent to other observers will be handled coldly and professionally by the OP. But that is an acceptable outcome. Professionals are allowed to be cold as long as they make it clear that this coldness is in the service of doing their job. Moreover after a few awkward exchanges like this, all but the most evil/deranged people will learn to stop pushing the button that is not getting the desired response.