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How should you handle a question in an interview for a PhD program when you don't know the answer ?

Should you try to just say something even if this is wrong or just tell the interviewer that you don't know the answer?

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Honesty talks, BS walks. – Daniel R. Collins Jan 30 at 20:20
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I refer you to the canonical text by Harry G. Frankfurt, professor emeritus of philosophy at Princeton University: amazon.com/On-Bullshit-Harry-G-Frankfurt/dp/0691122946 – Daniel R. Collins Jan 30 at 20:25
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What kind of question are we talking about here? It makes a huge difference. – Federico Poloni Jan 30 at 22:07
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"I don"t know." – JeffE Jan 31 at 1:41
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Look like you care, look like you feel you ought to know, look like you want to work it out straight away and will do in front of them immediately given half the chance. And don't forget to mention any closely related things you do know the answer to. – Lembik Jan 31 at 9:38

In most cases, the interviewer does not care about the "answer", but rather about how you answer. I would answer honestly with something like "I do not know, would you like me to try and work it out?"

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I am not sure that the interviewer won't care about the answer, but this is still probably the optimal strategy. – Bitwise Jan 30 at 20:53
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@Bitwise it would be very strange for the interviewer to not already know the answer to a technical question (unless of course it is truly impossible to answer). – StrongBad Jan 30 at 21:10
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Perhaps I misunderstood - I agree that the interviewer would usually know the answer. I meant that the interviewer will care whether the candidate does or does not know that answer. However, I can also imagine scenarios in which the interviewer actually does not know the answer - for example if asking about the candidate's past research. – Bitwise Jan 30 at 21:19
    
Yup. The idea is to find out whether you're curious and whether you are capable of learning. If you don't know outright, if they can lead a little bit and you can eventually figure it out, that's really good. – la femme cosmique Jan 30 at 22:39

Honesty would be the best and tactical strategy. No one is expected to know everything. An ideal panel would only be interested in how much you know and how much of that pertains to your candidate position as a PhD scholar.

The time given for you in the interview process is gold -- you must try to expose your potential as much as you are able to within the period. If you spend too much time in an a question you cannot make out the answer, then you are probably losing time to express the answers for the future questions you might know. Hence it would be better to admit that you do not know the answer and try if you are confident (as suggested by @StringBad) or move to the next possible question if not.

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I don't recommend lying but there is a saying "Nice guys always finish last". It's sad but true that the modern world values bravado over honestly and sensitivity.

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