The first time I took the GRE in 1973, I had a massive nosebleed and was terrified they'd see and make me leave so I didn't do very well on that I don't think :-) I retook it in the mid- to late-1990's and did okay, I'm sure my scores are still around here somewhere.

However, when I went to grad school, I went to my alma mater that didn't require tests, went on grades/success in undergrad school and let you "try" grad school if you wanted, provided you had graduated undergrad. I think I would go to a school like that, get the good grades and then "transfer" :-) if I did not want to continue at such a place. But, for a doctorate, the requirements are often a bit different, for many one has to have an advisor who'll take you before you get in, etc.