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The question is which system exacerbates inequality the least: On the one hand we have a well-known system with objective answers and a widely available study catalog, and on the other hand we have a system that largely involves administrators applying their subjective discretion to which extra-curriculars or essay is "best".

I am not from the US but I did appear for the SAT. The books are more than enough to get a very good score on the SAT. In my opinion, SAT is not difficult enough for coaching to make a very big difference.

Does it actually work?

These tests are notorious for having all the prep material in a few inexpensive books.