Good question ... and a lot of people have this question. Beware the answer is going to be a lengthy one as it is not so simple (for me) to answer it any other way.
It, of course, depends on the problem's structure on what strategy and methods to use to solve it quickly and correctly in GMAT. In GMAT you have less than 2 minutes per problem so you don't have a lot of time to do each step in the problem; a lot of the steps have to be done mentally for example multiplication, addition subtraction and some divisions, to name some. If you are unsure then use the scrap paper.
So now coming to your question about how do we know where to start. I will try my best to answer and be as generic as possible. In GMAT, particularly, what you can do is look and read the question and while doing so read the facts (given information) and see what it is asking you to find. I am sure you know this. Then look at the answer options and get an idea (kind of) what the answer’s structure or form is – this will partly assist you in figuring out what you need to do to do the problem. Most of the times what you have to do is to translate the math question into an equation(s) and then reduce it to the most basic form. If you see exponential type questions immediately start thinking of the exponential properties ( as in the problem above). Similarly in other topics of math start thinking of the properties of area where the problem is from. With practice this will become natural (almost).
If there are numbers and you know they can be factored down to smaller and easy to work numbers then do that. For example if there was (243)^23 you would not multiply 243 by itself 23 times would you? So some tricks that could help you would be: add the digits of the number up – so 243 would be 2+4+3 = 9 so we know 9 is a multiple of 3 so that means 243 is divisible by 3 – which means we can factor 243 in terms of 3 so in that case you would probably have to divide the 243 by 3 and obtain 81 so 81 times 3 is 243 but we know 81 is 9^2 which is in turn 3^4 – thus we get 3^5 which is 243 so then you can rewrite 243^23 as (3^5)^23 and leave it like that or sometimes you would have to write it as 3^115 (note here that you would want to multiply 23 times 5 mentally to be quick).
The other trick would be to see if the right most digit of the number ends in 5 or not; if it does then it is divisible by 5. Hence that number can be expressed as 5^n. If the right most digit is an even number then it is divisible by 2. Hence then the number can be expressed as 2^n. These are some of them that can help you in GMAT. I cannot remember all of them top of my head nor be able to write all of them here but on
https://beatthegmat.blocked there are multiple resources which are excellent and I personally found very helpful for GMAT prep.
So basically to summarize you have to make everything as simple as possible as then there is more clarity to the nature of the problem and thus the strategy/ method to obtain the solution will possibly come to you easily. GMAT is not about getting the correct answer but about knowing the fundamentals of English and math (– the 2 main skills needed as the foundation to learn everything else you will learn in MBA, so to speak) and to be able apply most efficient strategy/ method to efficiently solve the problem quickly. Something what an MBA person would do
. All that is needed is practice and keep track of errors you make during practice. Read all the explanation of the problems you have a tough time with and make sure you revisit them till you can solve them on the fly. Solving more problems will open you up possible methods (efficient ones) to solve problems.
Here is another link that may help you with numbers:
https://www.prepfortests.com/gmat/tutori ... properties
If you have a specific question from certain areas in GMAT math then post it and I will try my best to answer it.
Remember the rule is KEEP IT SIMPLE OR MAKE IT SIMPLE
Hope that helps!
Good Luck!
