What is the mechanism behind "gut feelings"? I'm thinking of a phenomenon that I've first observed in myself when taking an IQ test. Upon looking at the question, I selected an answer, but got this "gut feeling" or a hint that something was wrong with my response. Upon seeing the answers, the question was indeed answered incorrectly. I've observed this phenomenon several more times in different situations and can define it as a very quick flash of awareness or feeling that quickly subsides.

What is the neuroscience behind such "gut feelings" or "intuitions"? 

I'm particularly interested if such "almost" answers are some form of cognitive process, where some neurons fire, but not enough to produce a fully formed insight/idea/judgement.

Because the question that I was originally trying to answer was not lexical, but involved some rational thinking, I do not believe that this is exactly the "tip of the tongue" phenomenon.
Intuition and implicit learning

I recommend you have a read through Lieberman's (2000) review and theory article on intuition.

Lieberman argues that intuition is a cognitive and behavioural consequence of implicit learning processes. Intuition is contrasted with more deliberate thought processes. It also reflects situations where it is often not possible to articulate the reasons for a decision or belief.

These links with implicit learning are extensive. Much of skilled performance is performed automatically without conscious effort. We also build extensive associations between stimuli and decision relevant information. 
Furthermore, processes of learning can lead us to forget the reasons why something is true or why something is good, while retaining the fact that it is true or that it is good. 

Lieberman suggests various neural components important to intuition:


  It is concluded that
  the caudate and putamen, in the basal ganglia, are central components of both intuition 
  and implicit learning, supporting the proposed relationship.


Answering multiple choice questions

Your specific question concerns answering multiple choice questions. 

One explanation of the phenomena you describe is that you may retrospectively analyse your feeling of doubt once you know the correct answer. You may dwell more on your feelings of doubt when you get an answer wrong, but presumably are less likely to do so on the questions where you had doubt but ultimately got the question right. 

More generally, partial knowledge is not unusual when answering multiple choice questions. And presumably that feeling of uncertainty regarding the correct answer could come about by either deliberate reasoning or some intuitive unarticulated reason.  

References


Lieberman, M. D. (2000). Intuition: a social cognitive neuroscience approach. Psychological bulletin, 126(1), 109. PDF