The following is the list of universities that are among the top 50 in the US. To get admitted into these universities, you will need a very good GRE Score and very good academics. Overall student profile has to be really good.
Most of the American Universities require GRE for graduate admissions. However, GRE score is not the only part of the admission process, and therefore it is advised that one cannot apply to US university based on just the GRE score. To put this in perspective, a student with a 304 GRE score may get an admission into a university with 315-320 score bracket. While, a student with 325 may not get admission into the same university – This depends on several factors including student’s undergrad GPA, achievements, supporting documentation and more. Having said that, it is difficult to advise a student which universities they can apply without going through their overall profile.
Note: The following list of universities have been provided only for reference purposes. 
Here is a list of universities with a GRE score between 320 to 325:
Purdue University - West Lafayette
Type: Public
Location: West Lafayette, Indiana
Graduate Acceptance Rate: 27.5%
Graduate Engineering Students: 46% International Students
Tuition:  $29,134 per year (Full Time)
Minimum TOEFL Score: 77
Minimum IELTS Score: 6.5
Visit for more information – Purdue Admissions
University of Pennsylvania
Type: Private
Location: Philadelphia, Pennsylvania
Graduate Acceptance Rate: 23.7%
Graduate Engineering Students: 68% International Students
Tuition: $29,890 per year (Full Time)
Minimum TOEFL Score: 100
Minimum IELTS Score: 7.5
Visit for more information – University of Pennsylvania Admissions
University of Virginia
Type: Public
Location: Charlottesville, Virginia
Graduate Acceptance Rate: 22.4%
Tuition: $24,108 per year (Full Time)
Minimum TOEFL Score: 90
Minimum IELTS Score: 7
Visit for more information – University of Virginia Admissions
Rutgers University
Type: Public
Location: Piscataway, New Jersey
Graduate Acceptance Rate: 22.7%
Graduate Engineering Students: 56% International Students
Tuition: $26,736 per year (Full Time)
Minimum TOEFL Score: 83
Minimum IELTS Score: 7
Visit for more information – Rutgers University Admissions

University of Chicago

Type: Private
Location: Chicago, Illinois
Graduate Acceptance Rate: 20.2%
Graduate Engineering Students: 57% International Students
Tuition: $14,465 per year (Full Time)
Minimum TOEFL Score: 100
Minimum IELTS Score: 7
Visit for more information – University of Chicago Admissions
Northwestern University
Type: Private
Location: Evanston, Illinois
Graduate Acceptance Rate: 24.9%
Graduate Engineering Students: Not Reported
Tuition: $46,836 per year (Full Time)
Minimum TOEFL Score: 80
Minimum IELTS Score: 7
Visit for more information – Northwestern University
University of Massachusetts - Amherst
Type: Public
Location: Amherst, Massachusetts
Graduate Acceptance Rate: 25.5%
Graduate Engineering Students: 51% International Students
Tuition: $9,937 per year (Full Time)
Minimum TOEFL Score: 80
Minimum IELTS Score: 6.5
Visit for more information – University of Massachusetts, Amherst Admissions
University of Washington
Type: Public
Location: Seattle, Washington
Graduate Acceptance Rate: 22.8%
Tuition:  $28,425 per year (Full Time)
Minimum TOEFL Score: 92 (Minimum Test score needed for admission is 76. However, having 92 on iBT would  exempt from enrolling in the UW’s Academic English Program)
Minimum IELTS Score: 7 (Minimum Test score needed for admission is 6. However, having 7 on IELTS would  exempt from enrolling in the UW’s Academic English Program)
Visit for more information – University of Washington Admissions
Washington University in St. Louis
Type: Private
Location: St. Louis, Missouri
Graduate Acceptance Rate: 32.9%
Tuition: $45,700 per year (Full Time)
Minimum IELTS Score: 92
Minimum IELTS Score: 6
Visit for more information – Washington University in St. Louis Admissions
University of Arizona
Type: Public
Location: Tucson, Arizona
Graduate Acceptance Rate: 42.9%
Tuition: $27,700 per year (Full Time)
Minimum TOEFL Score: 79
Minimum IELTS Score: 7
Visit for more information – University of Arizona Admissions
University of Notre Dame
Type: Private
Location: Notre Dame, Indiana
Graduate Acceptance Rate: 18.8%
Tuition: $45,610 per year (Full Time)
Minimum TOEFL Score: 95
Minimum IELTS Score: 7
Visit for more information – University of Notre Dame Admissions
Rensselaer Polytechnic Institute
Type: Private
Location: Troy, New York
Graduate Acceptance Rate: 23.3%
Tuition: $46,700 per year (Full Time)
Minimum TOEFL Score: 88
Minimum IELTS Score: 7
Visit for more information – Rensselaer Polytechnic Institute Admissions
University of California - Irvine
Type: Public
Location: Irvine, California
Graduate Acceptance Rate: 20.28%
Graduate Engineering Students: Not reported
Tuition: $29,396 per  year (Full Time)
Minimum TOEFL Score: 80
Minimum IELTS Score: 7
Visit for more information – University of California, Irvine Admissions
University of California - Santa Cruz
Type: Public
Location: Santa Cruz, California
Graduate Acceptance Rate: 28.3%
Tuition: $26,322 per year (Full Time)
Minimum TOEFL Score: 89
Minimum IELTS Score: 7
Visit for more information – University of California, Santa Cruz Admissions
Universities for GRE Score 325-330Universities for GRE Score 330-340
Universities for GRE Score 315-320
Universities for GRE Score 310-315
Universities for GRE Score 300 to 310

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