Students are often concerned about their problem solving speed. This is understandable. Most tests are timed, and the graduate exams I teach require people to do math and logic problems much more quickly than they are accustomed to.
However, speed doesn’t come by simply trying to do the questions faster, or by tricks. Speed comes with fluency in the processes. Fluency means that a student is able to proceed smoothly from first encountering the problem to getting the right answer without pausing. If a student is fluent, they are able to speed up their problem solving, in the same way that a fluent English speaker can speak quickly if they choose to.
The importance of fluency is simple. There is nothing that makes a question take longer than a pause, and it is impossible to make a question go quickly if a student has to pause in the middle of it. In fact, trying to do a question quickly when a student isn’t fluent is a recipe for errors.
In order to promote fluency, I encourage students to achieve mastery of a question, and then to test their learned processes on other, similar questions. Any similar questions get entered into the error log.