My question is concerning learning strategy. I can solve the majority of the exercises in a typical graduate mathematics textbook like, say, Dummit/Foote's Abstract Algebra. To supplement my education (and, hopefully to increase my problem solving ability) I have been attempting many qualifying exams questions. Many are available online — as well as complete solutions. I find myself not being able to solve these — although I have the general idea in some cases. I am not particularly discouraged because I know these problems are not designed to routine; they are designed to ensure the student has an extremely deep understanding of the material and is ready for research mathematics.
My objective is to get to be better. I want to be able to attack these problems and solve them — or at least get closer than I am now.
The Question: To get better at problems like these, I would like to take a problem, give myself a time limit, say $3$ hours, to see where I get. Then, see (and study) the solution. Is this a reasonable strategy? I am looking for responses/advice from current PhD students studying for their exams and, of course, those who have passed such exams. My idea is if I implement the strategy above every day, there must be a point where I start getting better at these problems, right? (I should note that working on these has certainly made end-of-chapter problems look easy!)