the problems are conceptually easy but mathematically rigorous which means it take 10-15 steps to get to the answer , whether this kind of problems will appear in the PGRE exam or not ?
The problems in Kahn and Anderson's book definitely do overestimate the level of calculations you will have to do on the actual exam. With that being said, I think it's pretty dead-on in terms of content. Studying from the text will likely give you the best understanding of concepts (at least, I think it's worth looking over the latter sections on nuclear physics, special topics, etc. because these are great) and taking old released GRE's will give you an idea of the question type you'll see on the exam.
With that being said, the single best preparation (as in, the one thing you must do
before you take the actual exam) is to take the most recent released GRE exam. This should be the last thing you do before you take the exam, so if you're planning to study for a long time, save this one for the end, but this is a great representation of what you'll see on exam day.
Personally, I went through pretty much every chapter. You don't necessarily need to, but I think you would benefit if you have the patience. Don't let the problem difficulty discourage you, though; even the exams at the end of that book are much more computationally intensive (by K&A's own admission) than what you'll see on the real GRE.
Best of luck!