They use dry erase sheets. I believe you get six of them and you are not required to do it all in your head.

Go to the official site, www.mba.com -- there's a lot of good info about all aspects of the test.

I could not imagine trying to do it without scratch paper. That would be like an IQ test instead!

It's true that you get a sort of plastic-laminated paper to use as scratch paper. You write with a marker and you can't erase, so write LARGE! in case you have to cross stuff out - I think there is a definite correlation between writing tiny on scratch paper and making silly mistakes. You can always get more paper.

That said...

One of my GMAT sayings is that "if you find yourself doing lots of calculations, something is probably wrong". Many math problems can be solved without doing lots of math - sounds weird, but it's true. So, yes, use the scratch paper, but when you're studying, try to find ways that do not require calcs to solve problems. This will serve you well on the test.

Finally, start practicing now: put away the calculator and do all math in your head from now until your test date!