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The GRE is similar to the old SAT (before the latter removed quantitative comparisons and analogies--both of which are VERY coachable--and added Algebra II).
The analogy questions become quite easy when you use my strategies, even when you don't know all of the vocabulary. Just as in the math questions, you can work backwards to get the right answer, or at least better your chances.
Most tutors will tell you that the sentence completions don't lend themselves to strategies, and that you must just learn the vocab. While knowing the vocabulary helps greatly (see below), I suggest looking at the sentence as an equation--a self contained and precise equality (as precise as language can get).
Though I will offer the usual strategies you will find at Kaplan or Ivy West (remember, I train their tutors), as well as some that I have come up with on my own, what helps even more with all the verbal questions is to get inside the minds of the test makers. This may sound hokey, but if you consider that the questions go through several rigorous checks and balances, and that the test makers' job is to be as "objective" and irreproachable as possible, this knowledge can be a great asset when trying to figure out not only the right answers but the wrong answers as well. That said, you can see how my coaching will really give you an inside track!
The GRE math is much like the SAT math, requiring knowledge of basic math, algebra, and geometry. There are certainly tricks, but the greatest help is to review questions the student misses by and "typifying" them, so that the student can recognize it as a problem type, and then learn a specific process for its solution (and other's like it).
I am highly qualified in teaching composition, which is what I end up doing when I teach the essay parts of the test. I have worked to improve the compositional skills--grammar, diction, structure, style, argument, etc.--of literally hundreds of undergraduate students at UC Berkeley.