During my time as a political candidate I was fortunate enough to have a number of people on my team who were not only former candidates but who have made a career or working in politics, this meant that I was fortunate enough to get professional training through the election. However one of the best pieces of advice I received was also one of the simplest. When you don't know the answer to a question just admit to it, tell them that you don't know but if they are willing to talk to you after you can find out the answer and get back to them.
Now I understand that this may sound counterproductive in any context. And trust me in politics it doesn't make much sense at face value either. However I had a debate one evening and I can't remember the question that was asked but I genuinely didn't know the answer, the other candidates made up b.s answer's in an attempt to just fluff off the individual, I decided to go out on a limb and said "I honestly don't know, but come see me after and we can chat". That was it and I thought nothing off it...until after the event. Once we all got off stage and were just milling around chatting with people I had a number of people come up to me to tell me how impressed they were that I admitted to not knowing. I was told that it showed the sign of a mature and intellectual politician, and that they were relieved that I trusted that the audience was smart enough to know when I'm trying to dance around answering. Comments like that carried on for the evening and actually resurfaced in stories at other debates. I hadn't thought through the full meaning of me saying that "I don't know" but it had a huge effect on those that heard me. So I urge all of you to keep that in mind.
This is a piece of advice that will hold true in any circumstance. Assuming that people don't notice when they're being played is a costly mistake and has hurt many a smarter person than I. Treat those that you lead with respect, respect their intelligence most of all and they will reward you for it. At the very least they will not forget it.
With that being said; be careful. This only worked for me because I was very well prepared for the debates. I had an answer to everything else and people knew that. I only admitted to not knowing maybe two or three times over the course of the campaign, and never when it was truly important. Overuse this and you'll come across as unprepared and unprofessional. It's a last ditch effort but take it from me; it's a classy move and people will appreciate your honesty, in a profession like politics a bit of blunt honesty can be refreshing.