Applying to Mathematics PhD programs

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How easy or difficult is it to get into the following PhD programs for Mathematics with a 4.0 GPA, perfect GRE scores, and a few research papers at an average state 4-year university? I'm going to apply to all 12 apparently. This is the first stage of my career life.

Rutgers University-New Brunswick
University of Wisconsin-Madison
University of Illinois-Urbana Champaign
Purdue University-West Lafayette
Northwestern University
Northeastern University
Pennsylvania State University-University Park
Ohio State University
Washington State University
Louisiana State University-Baton Rouge
Iowa State University of Science and Technology
Rice University