I'm applying to graduate math programs and my subject test score was abysmal, but I'm very confident that I will have excellent letters of recommendation from my professors. Will these LOR offset the bad test scores? I know every situation is different, but in general what is your opinion?
4 Answers
Disclaimer: I am a current graduate student and my experience is limited to being the student representation on the graduate admissions committee of my program.
One of my advisers always reminded me of the following principle:
GRE scores will not get you in but can keep you out
What does this mean? GRE scores by themselves will never get you admitted into any program worth its salt. However, they do act as a nice way of filtering candidates, especially in schools which received hundreds of applications for its programs every year.
Once you make the initial GRE/TOEFL filter, you are good. Your application will then be vetted on the basis of academic achievements, research, statement of purpose and letters of recommendation. Ergo, if you are removed at the initial stage by virtue of your GRE scores being rather low, then chances are, that nobody will even look at the rest of your application.
However, if your GRE scores are bad (but not that bad) then your good LORs might serve you better in the later rounds.
Of course, for quantitative oriented programs (like math), you might be expected to get a perfect (or near perfect) GRE Math scores and respectable Verbal scores.
I hope this makes the process a little clearer.

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3What is an SOP? Please don't use abbreviations unless you are sure it's clear to everyone. – posdef Oct 21 '13 at 07:21
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Statement of Purpose. – math Oct 21 '13 at 07:27
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As @mathandzen rightly points out, its statement of purpose. This is a standard abbreviation in the context of American graduate school admissions. I have edited my original answer with the proper expansion. I hope that is helpful. – Shion Oct 21 '13 at 14:18
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2@Shion I had upvoted your answer the first time I read it, I think it's a useful and informative answer. My objection was not to the content, just to the liberal use of abbreviations. :) – posdef Oct 21 '13 at 15:44
You state yourself that every situation is different, and that really is all we can tell you!
At a school that receives a high volume of applicants, your GRE score is likely to matter a lot more than at a school where lower numbers of applications are received. An overworked applications committee is much more likely to toss an application with a low GRE score (without even reading the letters) than a committee that has enough time to properly assess each candidate.
GRE scores (can) matter a lot, and then once you pass the gatekeeper they don't matter very much any more.

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My reaction is pretty different from everyone else's here.
The short answer is: in my experience, yes, outstanding letters from credible, well-known letter-writers will outweigh poor GRE scores any day. Few applicants get really outstanding letters from a credible, trusted letter-writer, but when we do see a letter like that, it carries a lot of weight.
It does make a lot of difference whether folks on the admissions committee know and trust the judgement of the letter-writer. Does this letter-writer see a lot of students headed for graduate school, and see which ones are and aren't successful? Does this letter-writer work with graduate students? Does this letter-writer have a successful research program? Do people on the admissions committee know this letter-writter and trust him/her? What sorts of letters has this letter-writer tended to write for previous applicants, and if any of them were admitted, how did they work out? These factors weigh heavily in the admissions decision.
It also matters a lot what the letter-writer says in their letter. I don't know how you can possibly know how strong your letter will be. A letter that says "this student did really very well in my class" is actually a weak letter (contrary to what you might think), because it gives very little information beyond what is already on your transcript. In contrast, a letter that describes successful research you did with them and your contributions to the research project and how they were critical to the success of the research project carries a lot more weight.
Poor GRE scores might not trigger a kneejerk rejection, but they will certainly cause the admissions committee to ask questions and scrutinize your application closely before admitting you. "Why did this applicant score so poorly? Are they lacking basic knowledge? We'd better go look more carefully at their grades in their undergraduate classes. Is their poor performance on the GREs a hint of fundamentally insufficient preparation, or is it a one-off anomaly?" That's the sort of conversation you should expect committee members to be having. If the admissions committee can answer those questions to their satisfaction and the rest of your application package can survive close scrutiny -- if the rest of your application package is strong -- then I would not expect poor GREs to sink your application. On the other hand, if your GREs are poor, your grades are mediocre, and you don't have incredible accomplishments to counter-balance those flaws in your application, then you might be in trouble.
This is based upon my personal experience with one particular admissions committee, so I have a very small sample size. It is possible that other committees might do things differently.

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This varies wildly from program to program. Most people on admissions committees recognize that actual graduate work does not resemble a multiple-choice timed test given one Saturday... but there is difference of opinion about how much it means, exactly.
If you are from a good university with letter-writers who are well-known, terrific letters from them can substantially compensate for a terrible GRE subject test, although elite programs would still use the GRE as a "weeder".
So, in summary, it's hard to tell what will happen... but only a matter of degree, really, since there are so many factors in play. E.g., if your coursework background is solid and letters are terrific, and your personal statement is both very positive and perhaps notes that you feel your performance that day did not indicate your preparation or ability, chances are only slightly worse...

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