Re: quantitative:
Part of it is problem solving ability, I agree, but you can't do much creative thinking on GRE quant questions without a basic math foundation. It's necessary to have both learned
and retained the algebra, geometry, and arithmetic skills from grade school, high school, and/or early undergrad. For some of us (*coughcough*), it was in one ear, retained just long enough to scrape by, and out the other ear, and with little use as possible thereafter.
😉 I know firsthand that there is a required, solid foundation of mathematical concepts that are absolutely necessary to have memorized and easily recalled to at least get a passable quant score. I had to relearn many of those ... and sans calculator.
Holy moley, do you know how long it's been since I've added fractions, or fiddled with exponents without a calculator, or done long division by hand?! I was probably in fifth grade. And I wasn't even that good at it then! I also had to learn (actually
learn! the nerve!) all those geometric formulas and special triangles that I've always just referenced on the inside cover of a textbook or on a formula sheet for an exam.
Yeah, I'm a little bitter about the GRE quantitative portion.

It's definitely not the strong point on my app!