estode wrote:Is there a short way to check if 7!-1 is prime?

There's no fast way (without a computer) to demonstrate that a large number (like 7! - 1) *is* prime, though it is often easy to prove that a large number is *not* prime (if it's even, for example). To prove a large number is prime, you really have to try dividing it by every prime up to its square root. The square root of 7! - 1 is just less than 71, so to prove 7! - 1 is prime, you'd need to try dividing it by every prime up to 67, which is a long and boring process. You won't ever need to do that on the GMAT.