Generally, PhD programs in the US have many more applicants than they can accept. The number of positions is limited by finances (a department can only afford a limited number of RAs and TAs), space and resources (students often need offices and access to equipment), and the ability to supervise the students (there is a limit to the number of PhD students a faculty member can effectively supervise). The admissions committee must decide which of the qualified applicants are most likely to be successful researchers while taking departmental "politics" into consideration. These politics include things like the start up package for Professor X included a funded PhD student and a particular resource is already at capacity.
The admissions committee bases its decision on a number of pieces of information including GPA, GRE scores, statement of purpose, references and interviews and for international students TOEFL scores. There is no formula (e.g., 6*GPA+1*GRE+2*References+Publications) by which applicants are ranked, but some universities and/or departments set minimum requirements (e.g., GPA over 3.0 or a TOEFL over 85). The admissions committee looks at the entire application to make an informed judgement. This means that being strong in one area can, and does, offset being weak in another area.
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