<p>From what I understand, doing well on the quantitative section of the general GRE is necessary but not sufficient for your application to be considered seriously at top pure math PhD programs. Most top 20 math programs I’ve looked at report that the median Q score of their entering grad classes is in the 790 - 800 range. If you’ve got a Q score in the, say, 770 - 800 range, you then also need to do well on the Math subject test GRE. This is a very hard test, reportedly the hardest subject GRE there is these days. Although the grad programs will say things like the subject test GRE score is not that important, from what I’ve seen you need to get a percentile score on the math subject test in the 80% or higher to be seriously considered at the top programs. Berkeley makes this explicit.</p>
<p>Again, from what I’ve seen, you really need to study for the math subject test, and not just for a week or two, if you want to do well (80% or higher).</p>