I would preface what I'm about to say with this: I generally believe that it's harder to improve in verbal than it is to improve in quant. That doesn't mean you should feel discouraged, but be ready to put in the work and only see slow gains to your verbal score. You can definitely get a 40+V score as a native speaker with 3 months of studying.
Now quickly go over a few of your questions:
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I don't really have a strategy for approaching the SC questions.
Search GMATClub for the "splitting" method for SC. That should be a great starting point for SC. You also need to read up on SC "theory" to really make gains in the section. Subject/verb agreement, proper punctuation use, dependent/independent clauses, etc. The
OG is a good place to start for that stuff.
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I am at the moment considering
e-gmatI've heard great things about their course.
Magoosh also would be a cost-effective way to gain access to lessons and questions. In all honesty, I would hold off on buying extra resources for verbal until you work your way through at least the
OG. It'll give you extra time to really figure out where the best value is for resources/courses.
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Also I know a lot of people say focus 1st month on quant 2nd month on verbal etc
I don't like this strategy. I think it's better to constantly build on your skills in both sections, rather than do one, leave it, then return to it. You don't want to have to relearn in the third month some of the things you learned in the first month of studying.
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Also how can I get walkthrough solutions to the CAT questions on the GMAT PREP programme
Type the first ~5-10 words of whatever question you want into google. Click on the GMATClub link that pops up. Scroll down, find Bunuel's answer, rinse and repeat.
But seriously, I wouldn't recommend using the
OG to explain answers you got wrong. I found their answers to be unintuitive most of the time, especially on stuff like SC.