Logic v/s. Method

I face this problem so many times when I was preparing my self for competitive exams and also at school level. In school my math’s teacher was focusing on method while I was focusing on logic and for doing that I suffered from defame so many times.

I was used to do sum with my logic because frankly speaking remembering a formula was not easy work for me. Even in papers I used to do sums with my logic.

I thought so many times on logic and method? Which one is right?

And after all the answer which I got is neither a logic nor a method is important. The important is answer.