I only got a 33 (12 PS, 10 VR, 11 BS), but I under-performed on VR and neglected organic chemistry during my preparation (missed around 5 super easy organic chemistry questions on the real thing).
I don't think you need to be a genius (or even be very smart) to score a 35+. For the sciences, you can realistically aim for a 12 if you thoroughly grasp the content and do an extensive number of practice passages. Taking all the AAMC exams under realistic conditions is also a must. As long as you are not terrible in the sciences, a 12+ in PS and BS is very doable. The PS section is the easiest section in the whole exam, and I would go further to say that most people can realistically aim for a 13 on PS.
Verbal is somewhat trickier. You can't really prepare for this section in the traditional sense, but you can, again, do an overwhelming number of practice passages. Reading rigorous material on the side can also help. Unless you struggle significantly with reading/analyzing English, a 10 in VR is absolutely doable.
So if you add up everything together, you'll see that with thorough preparation, substantial practice (passages and all AAMC full lengths), and maybe a little bit of luck, a 35 is a realistic score. I wasn't that far off, and I definitely slacked off/cut some corners during my preparation. I definitely prepared pretty adequately, but I didn't work nearly as hard as I could have.
Best of luck!
EDIT: Now, if you want to score in the upper 30s/lower 40s, then I do believe that you'll need a certain degree of innate intelligence and a fair dosage of lady's luck! But a 35 is well within the achievable range of the average premed student.