The GMAT is not a test of whether you are a human calculator, so the answer is 'not many'. Most prep books recommend memorizing far more than is actually ever useful. You certainly want to know your multiplication table up to 12x12, perfect squares up to 15^2, perfect cubes up to 6^3, and the small powers of the three smallest primes (the first eight powers of 2, probably, and the first four powers of 3 and 5). Besides the most basic fraction/decimal conversions (1/2, 1/3, 1/4, 1/5, 1/8, 1/10, and similarly simple conversions) I have never needed to know any fraction/decimal conversions on a GMAT question. It can also occasionally be useful to know rough estimates (to one decimal place) for sqrt(2) and sqrt(3) and Pi, and you should be able to recognize small prime numbers (up to 50 or so).
I suppose in very rare questions it might be helpful to know a bit more than this, but it surely is not 'indispensable' to success on the test, particularly if you know enough basic arithmetic to work out what you need fairly quickly.
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