Given that I scored 1530 on my SATs (790-V/740-M) and a 34 on my ACTs (36-V/32-M splits) while at USMAPS, I joke that going to Columbia made me stupid. I don't really believe that, though. Here are what I consider the real factors in my disappointing GRE score:
The totality of my studying for the GRE amounted to a cursory review of basic math concepts in my study guide right before I took the exam. I was rusty, to say the least. As my first GRE, I rationalized that I could treat it as a $140 test event, to use an Olympics term, to familiarize myself with the exam experience.
I believe I lost points in the GRE's new computer-based format. I didn't mind answering questions on a computer; it took some getting used to at first since I grew up on paper-based standardized exams, but it was a painless adjustment. I lost points because the new format didn't allow me to go back to a question after confirming an answer. On my previous standardized tests, like the SAT, I would routinely go back to questions I was uncertain about and change at least 2 or 3 of my answers. On the GRE verbal section, I had 10 minutes left at the end, which I would have used to check over my reading comprehension answers and puzzle over the harder vocabulary questions. On at least 1 math question, I realized the correct answer the second after I pressed 'confirm', but it was too late to change it. I suppose a test designed to adjust the questions after each answer can't work if we're allowed to go back and change answers.
I slept for 2 hours and not well before the exam. I felt alright at the start of the test, but once I started to tax my brain, I felt dazed. I don't believe my verbal score, except possibly the reading comprehension, was hurt much by lack of sleep, but my punchiness definitely degraded my math calculation speed and acuity. It seemed as though every time I looked up from my scratch paper after kneading my brain through even a relatively simple calculation, 4 minutes had passed when I could only afford to spend a minute-plus on a question. I don't know yet whether my lack of sleep hurt my writing score.
I underestimated the difficulty of GRE math. The people I asked told me that GRE math is no harder than SAT math. The study guide I used downplayed the difficulty further, even going so far as to claim the GRE used junior high school level math while taking into account students who take minimal math in college. My impression is that the GRE math section requires far more speed than the SAT and uses trickier questions. I ran out of time and left questions unanswered, and felt bewildered by too many of the questions. That said, I was rusty and sleepy, so it's possible my perspective was skewed; the key to answering a GRE math question is immediately understanding the question and recognizing the solution, which my brain was not equipped to do yesterday.
My 720 verbal score is lower than I would have liked. I don't know that I would score better with more sleep and preparation, though. The GRE reading comprehension questions were somewhat more advanced than their SAT equivalents and I would have spent more time on them if I knew beforehand how much time I would have left at the end of the section, but they weren't too hard to adjust to during the test. I believe scoring better would depend more on my luck with the vocabulary rather than better preparation. For example, I scored a 700 verbal on my SATs in high school and improved to a 790 verbal at USMAPS. I don't believe my verbal ability increased between the two SATs; I think I was just luckier with the questions.
My 650 math score feels like winning a bronze medal in the Olympics. I'm thankful it wasn't worse and it's an achievement given how poorly I thought I my score would be while taking the exam, but I'm disappointed I didn't do better.
If I use my first GRE experience, practice and study, and make sure to have a good night's sleep beforehand, would I score better if I took the GRE again? Yeah, probably. But, depending on my writing score, my first try at the GRE is respectable. When I receive my official scores, assuming my writing score is also respectable, I'll use them to apply to grad school and see what happens. If they're good enough for the schools, then they're good enough for me.
Update: I scored 5 out of 6 on the written portion. Yikes - I expected at least a 5.5.