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By any chances, what do you suggest for improving my quantitative score? I took a lot of math courses in college, so I had alot confidence in my mathematical ability. With that in mind, I did not spend much time to study for quant section at all for the two previous attempts (During these two tests, I spent so much time using long and tedious calculations to solve the quant problems
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There is no wonder that math gurus don't ace the quantitative section. I know a math genius who got 760 on the quantitative. It's not about measuring your mathematical abilities . It merely tests your ability to solve problems in limited time. And that's why you only encounter high school math questions.
Preparation for the quantitative section shouldn't be hard on you, specially because you have taken many courses in calculus. You only need to practice for the test and to learn some hacks and techniques that gives the ability to finish the test on the time. I have encountered some threads on the Quantitative Preparation Forum that lists some tips and hacks, you may have a look on such threads.
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I may possibly get lower score on the verbal because English is my second language
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I am really impressed by the advancement you achieved in raising your score from 360 to 620, and I would like to know how you did so because I'm not a native speaker and my Verbal score was abysmal too. Anyways, as long as you stays in the 500ish level there is no need to be worried because the committee is not expecting more than this score.