So if one answer is x^2+y/sqr(z) and another is 15y/sqr(z) and a third is 15/xy/sqr(z), then they suggest c because you have the most elements in common with the other answers, 15, x, y/sqr(z). This is literally in a McGraw-Hill (one of the 3 big billion-dollar education publishers) book on the GMAT.
It has nothing to do with any real world, practical application, and it's completely different from what you describe which are completely sensible approximation techniques. These aren't approximation techniques, they're guessing techniques and it's total bs. It's not teaching you a strategy to learning, to approaching problems to find meaningful solutions, or to approximate answers to questions, it's teaching you purely to game a test and the real world doesn't work like that.
I would hope in later chapters they talk about good approximation techniques, and leave the similarities technique as an absolute last resort.
In tests specifically, you can usually knock out a couple obvious wrong answers. Then, if you are still not sure, you are supposed to decide which is the best answer. You take a risk with that decision.
To give an analogy from programming, say you are not sure of which algorithm applies best to a situation. You are stuck between two solutions which both look good. You can either stay stuck all day meticulously deciding which is best, or you can actually get work done and take a risk on which one you feel works best in the situation.
If you take your time on deciding which works best, surprise, a competitor took a hunch on a solution, got to market first, and put your company out of business. It doesn't even matter if your solution was better in the long run. (See: Windows vs Mac OS in the 90s)
It's not just blind guesses. It's deciding which guess gives you the best chance of getting it right. This is what 'guessing technique' is about. Of course, you don't go in to a test not knowing anything at all, then you will end up at the 20% of a completely random guess. You go in with a solid foundation, giving you the ability to answer the "easy questions", and giving you the tools you need to get "50% of higher" on the other questions.
"So do I want to take a risk?" Absolutely, you do. Nothing ventured, nothing gained. The alternative is extreme grit and reinventing the wheel, which (for the vast majority of people) leads to quick burnout and psychological issues.