As an "INFJ" who has learned to think in an "INTJ" way through doing a maths degree and hanging out with INTJs, I also agree that different ways of problem solving can be learned. What I tend to find is that my intuitive way of thinking gets me a less accurate, faster answer, which is in keeping with what everyone else has suggested.

However, with my intuitive thinking, there is also an unusual quirk that although my strongly intuitive responses are fairly inaccurate (correct about half the time), this is much more accurate than they have any right to be given the precision of the ones that are correct. My intuitive thinking usually applies to people and their emotions, and I frequently get very specific hypotheses about the relationships between a set of people. Learning logical thinking has allowed me to first highlight hypotheses with intuition, then slowly go through and falsify the wrong ones, which leads me to an answer that I think I couldn't possibly get with logic alone, since my intuition uses things like facial expressions and body languages and voice inflections to gather much more data than I could consciously.