There really isn't a shortcut to math. I can tell you what to read in order to understand these questions, but it might take you a few years.
My complaint was not about these questions. These are M.Sc. exam questions and it should take you years of study to undertand and be able to solve them.
My complain was about math communication in general. It shouldn't take me years of study to understand a question on a basic level. I gave the example of prime factorization earlier but you can think of how most math problems are communicated to the general public.
A great example to illustrate my point is Project Euler. The way problems are communicated on PE is vastly different than the way they are communicated by professors, wikipedia or most other outlets. Every problem there starts with an introduction followed by a set of assumptions and a posed problem to be solved. It is far more friendly and inviting of a way to communicate math problems to the general public!