The GRE is a U.S. standardized test administered to students who wish to apply to graduate school in fields other than law and medicine (which have their own standardized tests—the LSAT and the MCAT), for the benefit of graduate school admissions offices that want to gauge how students from very different academic backgrounds fare on the same wide-ranging test.
Since the GRE is aimed at students who have completed or are near completing four years of collegiate study, you might expect the test questions on English to be sufficiently sophisticated and challenging to be of interest to participants at EL&U. But unfortunately, the GRE suffers from the same drawbacks as other standardized tests—most significantly, that each question included on it is designed and calibrated to draw a certain proportion of incorrect answers.
The goal isn't merely to see whether test takers recognize a particular syntactical or vocabulary shortcoming in a question, and know how to improve it. Instead—at least in some questions—the point is to gauge how well the test taker keys on some hint or tertiary aspect of the sentence or passage in the question to conclude that one of the five optional answers is better than the others.
In such situations, to my mind, the test isn't testing English language and usage, or reading comprehension, or anything else beyond the test taker's ability to analyze which answer the test creator has set up as the correct one. Consequently, these questions are a bad fit for our site because they don't involve grammar (broadly understood) or usage.
Even the questions that clearly do have an objectively defensible best answer grounded in language and usage may not be much good as a means to teach about or explain the underlying principle of language because, again, the false answers are framed in ways to make them plausible (or at least ambiguous) so that significant numbers of test takers will choose the wrong one; and the right answer may be far from optimum so that it doesn't stand out too strongly against the others.
To me, the greatest problem with the GRE (and the SAT, and the LSAT, and the MCAT) as it applies to English is that it supposes that mastery of the language can be adequately gauged by offering test takers one supposedly right answer and four supposedly wrong ones to each of a series of discrete questions. This is not a fruitful way to approach English, in my opinion, and analyzing why the supposedly correct answer is (d) and not (a) is not particularly fruitful or meaningful either.
A dedicated Standardized Tests SE would no doubt draw numerous thoughtful answers to the task of analyzing why particular test questions are framed the way they are, and why the test creator considers one of the answers to be the right one. But at EL&U, I think, the task is only marginally related to our focus on English language and usage, and such analyses are in fact counterproductive because they encourage a false notion of what it means to have a firm understanding of English. I would be happy to see no more GRE questions on this site.
