How many math PhD spots are offered each year by the top 50 US programs?
If all you're interested is a ballpark number, then here is one way to estimate: At Texas A&amp;M, the math department hires 20-25 graduate students every year. (We make about twice as many offers.) If this was representative, then the top 50 schools would hire 1000-1250 students each year.

Now, A&amp;M is a big department (~85 tenure track faculty). Most departments will be smaller, but in the top 50, most will be at least half the size. So my best guess is that the top 50 programs together will hire ~750 students each year, plus or minus maybe 250.

(And, for comparison: Practically all of our hires have a Quantitative GRE score above 163. This coincides with about the 85th percentile.)