My way of Thinking

I had this conversation with a friend, that has set me thinking, and I am still searching for answers.
You see, we have this class, were we learn how to solve question that we would be asked in the aptitude tests, in the various placement interviews. These questions are the usual CAT type Quantitative questions, which are concerned with using some basic concept of Maths, like SI, percentage or GCD/LCM ect. Now you all know that I would not be having any problems with this, and you are right. I treat the whole lecture like a long and drawn out Puzzle session, and try to solve the questions in as many ways as possible. Very often it happens that I solve it much before anyone else, and sometimes even before others have started working on it.
It was regarding this that we were talking. She asked me, "Are you studying for these problems?" I said "no". She then asked me how I could come up with solutions so fast. Before I could answer that, she said, "Everyone requires time to think with logic"

This is when I realised, how differently I think when compared to most people. I tried to answer her question, but I could not articulate myself properly, so she was rather unsatisfied. So let me try to say here what I wanted to say.

I do not think with logic, I just think. Very often, my thinking is not logical; it is a series of random unconnected thoughts. But that is besides the point.
I do not need to think to solve these elementary problems. I can see the solution. It is after I see the solution, that I have to convince myself, which I do by thinking. There could be many reasons why my brain works like this.

Firstly, I have been solving puzzles for a long time. And compared to them, these problems are very simple. Hence I can quite easily abstract the mathematics out of it, and form an equation.
My experience also helps me out here. It tells me the best way of solving the equation, and shows me any short-cut, if any exists.

Further, more, I have always played around with numbers and am not scared of them. This might seem trivial, but I know so many people who do not realise what numbers are, and are more caught up in their properties and characteristics. Let me illustrate with an example. For me, 0.7, 70% and 7/10 are the different aspects of the same thing. I can use them interchangeably, because I am manipulating the Number underlying these representations, not the symbols. I am surprised when people say, "Why are you using 0.7? The question says 70%." This point is an important point, which many people like us, fail to grasp.

Further, more, once we have converted the problem into the language of maths, it can only proceed logically; there is no other way. I realise that I have so internalised this language, that I do not have to work at it, it works through me.

However, is this just a result of familiarity, where I have internalised so many things, that they seem natural (like we have memorised tables, and have no problems believing 3 times 17 is 51). I think not. I think there is something deeper. This is where I am having problems with articulation, and will be quite helpful, if you help me out.

As I see it, my thinking, is different from my expression of thinking. So When I say that I see the solution, I mean that my brain-processes are unconscious. I do not need these symbols, laws, and rules. They are followed implicitly. It is when I convey my thoughts to others, that I need these symbols and rules.
That is where the 'Think logically' comes in. That is where one is in control of thoughts (I'll prefer to say that one can choose which thought to focus on).But for greater part of my conscious time, I do not think consciously.

I'll illustrate this with an example. When I am on the bike, and taking a turn, I have to bend inwards. This I do without thinking. Even the amount of leaning is unconscious. A similar thing happens while walking and jumping. If you just try to think of what you are doing when you do these things, you will be surprised by the number of decisions you are taking, and how fast you take them.

I guess my rational processes also are performed at the same baser level, and by training and experience, I am capable of expressing them in a verbal way.