picking numbers

I think the thing here is to pick numbers first because it gives you a very intuitive understanding of how the problem works. A lot of the times, actual solutions take way too much time and you'll end up wasting time that could be better spent on a question that really requires you to make use of such computational methods.

However, if your preferred method is to solve everything (like me) I understand it takes a bit of time. But the key here is to understand that GMAT tests you on how quickly you get the right answer and move on to get more right answers. In other words the GMAT Math tests you on how much GMAT Math you know, and is no indication of actual math prowess. I suggest you get used to the tricks used by GMAT Club or by another prep strategy book/class rather than try to find a complete solution all the time.

That said, it never hurts to look for a theoretical explanation once you get an intuitive understanding of the concept just to reiterate.