Based on my experience of helping students with the GMAT test, I have found that focusing on advanced problem solving skills is essential to push students to a score of Q50/Q51. Many of the students who end up scoring very high on the GMAT often come in with prior experience with problem solving. The question is what is Problem Solving? Here is a brief article by Richard Rusczyk on What is Problem Solving? I consider effective problem solving to be a set of skills that is a combination of flexible thinking, ability to quickly list a set of approaches to a problem, being able to approach a problem from different angles, and also possessing the accuracy and speed to implement the necessary steps.
The question is how is all of this relevant to the GMAT? Most problems on the GMAT Math are straightforward, however when you reach the upper percentiles of the score scale, you will typically encounter about 8 to 10 problems that require the necessary problem solving skills. The problems on the GMAT are typically not very hard because on average one only has two minutes per question. To help prepare students for targeting these problems I use the American Math Competition(AMC) problems to help students enhance their problem solving skills. These are an excellent set of problems that are written by a very bright group of people, consisting mostly of Mathematics professors in United States. I have gone through the past exams and I have curated and collected a set of problems that I believe would be beneficial to students going for a high score on the GMAT. I have only collected those problems that use the same set of basic knowledge that the test writers test on the GMAT, this means no problems involving trigonometric functions, complex numbers, etc. I do want to point out that many of these problems are fairly challenging and I urge you to struggle with them, because that would help you to hone your problem solving skills.
You can access these problems at the following link: AMC Math Problems for GMAT Math. They are categorized by topic. There are no explanations at the moment, but I will be adding video explanations to these problems over time.