Note: The information below is dated (to like 2018). I know some of the GRE materials referenced have improved, and some have moved (so some links may be broken). Sorry.
As part of the 2017 and 2018 University of Chicago REU, a series of preparation sessions were run. To this end, a large set (consisting of at least 100 problems) was created. These problems were intentionally created to be much more difficult than standard GRE problems, and thus have little intersection with other preparatory material. Thus, find below these sheets, along with: a treatise of our opinions and advice on the GRE and studying for it (including comments on some other preparatory material), the official released tests, and links to some other preparatory material.
This document contains our advice and opinons on the GRE and studying for it. This includes a review of some of the other preparatory material, and an exposition of the philosophy behind our own study materials. (Note that this advice is as of 2018, so some opinions on study materials may be out-of-date.)
The following are links to our materials. We presented these in sets of 22 questions. The final set is not 22 problems, and consists of the extra problems that were not placed in a set; thus, no promises are made as to the quality of these problems.
The following are the officially released tests from ETS. One is released about every 5-7 years. Note the first two digits in the number code correspond to the year of the test.
It should be noted that GR1268 and GR1768 are THE SAME TEST. I don't know why they bothered releasing the same test. It should also be noted that the percentiles are different across GR1268 and GR1768, with people doing significantly (about 4 points) better on the later test. This gives some approximation about the trend of score. Thus, you should use GR1768 to score yourself. Both are included below, for completeness.
We include here some links to other preparatory material. For our thoughts (a review, if you will) on some of these materials, see our causerie above in the Advice section. Note there is no inherent order to the material, just the order I remembered its existence.
There are also other small collections of notes and problems. If you know of some source that you would like to be included in the list above, feel free to email me.