I very much doubt that most college students today, even in technical majors, could work out the geometry proofs. I was a calculus TA for two years in college (at an engineering school), and students don't know geometry anymore. Nor can they prove anything at all.
Not sure why this is, or was, getting downvoted. For most high school students, geometry consists of 1 semester in their entire high school career, and it mostly involves learning about triangles and polygons and learning the (n-2)/180 formula and a few, trivial proofs. The depth of Geometry on the Harvard test is not very deep per se, but it's easily out of reach for most high schoolers.
Now the students who do math contests and are AIME/USAMO level could probably do the geometry section here without a lot of trouble, but they are the exception.
If things continue as they are, expect this to change a bit. In particular, proofs like #4 on Geometry is going to be a requirement in 45 of the 50 states.
