Comprehensive/ Qualifying Exam

[SKS2s17fa]

I am a master student in math in a US university and I want to apply for PhD in pure math. I have passed the comprehensive exam this summer, which covers all first year graduate classes. How does this help for my application?

[6ix9ine]

Quite a few people drop out of PhD programs because they aren't able to pass the qual.

[SKS2s17fa]

So how good is this result? What level of schools should I expect?

[Orpheus11235]

Impossible to tell without more detail. For instance, passing a comprehensive exam at a rank ~100 school will probably do nothing for your application to top 20 schools. Also, this is a very small part of your application. What matters more is your overall academic performance, any research experience, and letters of rec.