I will give you my take on how to jump from Q50 to Q51. First if you are consistently scoring Q50, then that means you have all the basics and the advanced ideas in place. It is also possible that there may be some subtopics where you are not as strong as others. Clearly beefing up on those would be a good strategy.

As for the specific problem types, there are two category of questions that can hold you back from a Q51. The first ones are the medium level ones where one could misinterpret a statement and fall for a trap. These are problems that you know everything about but still trip on something small and make a mistake. These are really hard to correct, other than having extreme focus and double checking your work. This can happen to anyone on any day. I personally double check the easier problems, because I know I am more likely to miss an easier problem than a hard one. The reason is that the harder ones rely on testing an advanced concept and rely less on how the questions are phrased or need to be interpreted.

The second category of questions that mostly rely on a new idea require you to be fairly flexible in your approach. These questions often rest on testing an idea that you may not have seen before. Of course, they are not entirely new, but are significantly different than what you may have seen in practice tests. To be able to deal with these problems, I generally recommend going one step beyond GMAT, this where others may disagree with me. I will illustrate with an example. Let's say I want to push my understanding of Counting and Number Theory. I would give the following question to a student(Source American Mathematics Competition AMC 12 2003 Problem#23):

How many perfect squares are divisors of the product (1!)(2!)(3!)(4!)(5!)(6!)(7!)(8!)(9!)?

(A) 504 (B) 672 (C) 864 (D) 936 (E) 1008

This problem is beyond what you would encounter on GMAT, however it has the elements of the concepts necessary for the GMAT, and it does an excellent job of forcing you to think and come up with an approach to solve this problem. This struggle that is inherent in solving this problem is extremely valuable for those few hard problems on the GMAT that determine the difference between Q50 and Q51.

Cheers,
Dabral
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The question is, is there any point trying to push 50 to 51. There are 2 types of Q50, one where you are making 2-4 mistakes and other when you are making 5-8. If you are making less than 4 mistakes, Q50 and Q51 will give you same overall score keeping the verbal score constant. Google Q50 V35 - 710 and Q51 V35 - 710.
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It's easy to say you can't do it , you are not good enough.
It's much harder to step in your shoes and work to the point of achieving it.

I agree with AbhiJ here. You might want to rethink the return you will get by putting in extra effort to push the Quant score from 50 to 51. In the eyes of the adcom, Q50 and Q51 are the same. People who are on the higher rungs of Q50 on a particular day could be on the lower rungs of Q51 on another day. You may actually score Q51 on the test day, who knows! A 1 point increase in the Q score will hardly affect your overall GMAT score. On the other hand, you might want to put in extra effort in Verbal. An improvement in the verbal section could make a lot of difference.
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Dabral, thanks for cherry picking the problems and listing down along with the answers. Those looks like a great practice!
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Thanks,
PraPon

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