The GMAT does not test whether you're a 'human calculator'. While you do need to be completely comfortable multiplying small numbers -- you shouldn't need to think about what 8x7 or 11x12 is equal to -- you won't need to multiply two awkward large numbers, or square any awkward large number. On some questions, it may, at first, appear that you need to do a strenuous calculation, but there will almost always be a way to avoid it. For example, you might be asked to find:
3201^2 - 3199^2
Of course, we could square 3201, square 3199, then subtract, but that could be a lot of work. Instead we can notice that this is a difference of squares:
3201^2 - 3199^2 = (3201 + 3199)(3201 - 3199) = 6400*2 = 12800
If you have a lot of time to study, there's no harm in learning the sorts of tricks you mention, but there are certainly more important things to know.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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