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 good GRE Score and good academics. Overall student profile has to be 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 315 to 320:

Pennsylvania State University - University Park

Type: Public
Location: University Park, Pennsylvania
Graduate Acceptance Rate: 21.9%
Tuition: $33,386 per year (Full Time)
Minimum TOEFL Score: 80
Minimum IELTS Score: 6.5
Visit for more information – Pennsylvania State University Admissions
North Carolina State University
Type: Public
Location: Raleigh, North Carolina
Graduate Acceptance Rate: 16.8%
Graduate Engineering Students: 58% International Students
Tuition:  $21,311 per year (Full Time)
Minimum TOEFL Score: 80
Minimum IELTS Score: 6.5
Visit for more information – North Carolina State University Admissions

Ohio State University

Type: Public
Location: Columbus, Ohio
Graduate Acceptance Rate: 16.7%
Graduate Engineering Students: 57% International Students
Tuition: $1029.15 per credit (Full Time)
Minimum TOEFL Score: 79
Minimum IELTS Score: 7
Visit for more information – Ohio State University Admissions

Boston University

Type: Private
Location: Boston, Massachusetts
Graduate Acceptance Rate: 24.8%
Graduate Engineering Students: 38% International Students
Tuition: $45,686 per year (Full Time)
Minimum TOEFL Score: 84
Minimum IELTS Score: 7 (Students seeking financial aid should have 7.5)
Visit for more information – Boston University Admissions
Vanderbilt University
Type: Private
Location: Nashville, Tennessee
Graduate Acceptance Rate: 14.7%
Tuition: $1,782 per credit (Full Time)
Minimum TOEFL Score: 100
Minimum IELTS Score: 7
Visit for more information – Vanderbilt University Admissions
New York University
Type: Private
Location: Brooklyn, NY
Graduate Acceptance Rate: 50.7%
Graduate Engineering Students: 43% International Students
Tuition: $1,452 per credit (Full Time)
Minimum TOEFL Score:  80
Minimum IELTS Score: 6.5
Visit for more information – New York University Admissions
Virginia Tech
Type: Public
Location: Blacksburg, Virginia
Graduate Acceptance Rate: 20.1%
Tuition: $26,754 per year (Full Time)
Minimum TOEFL Score:  87
Minimum IELTS Score: 6.5
Visit for more information – Virginia Tech Admissions
University of California - Santa Barbara
Type: Public
Location: Santa Barbara, California
Graduate Acceptance Rate: 15.1%
Graduate Engineering Students: 60% International Students
Tuition: $28,216 per year (Full Time)
Minimum TOEFL Score: 100
Minimum IELTS Score: 7
University of California - Davis
Type: Public
Location: Davis, California
Graduate Acceptance Rate: 24.3%
Tuition: $28,211 per year (Full Time)
Minimum TOEFL Score: 80
Minimum IELTS Score: 7
Visit for more information – University of California Admissions
vUniversity of Southern California
Type: Private
Location: Los Angeles, California
Graduate Acceptance Rate: 32.1%
Graduate Engineering Students: 67% International Students
Tuition: $32,747 per year (Full Time)
Minimum TOEFL Score: 90
Minimum IELTS Score: 6.5
Visit for more information – University of Southern California Admissions
Michigan State University
Type: Public
Location: East Lansing, Michigan
Graduate Acceptance Rate: 11.4%
Graduate Engineering Students: 53% International Students
Tuition: $23,756 (Full Time)
Minimum TOEFL Score: 80
Minimum IELTS Score: 6.5
Visit for more information – Michigan State University Admissions
University of Cincinnati
Type: Public
Location: Cincinnati, Ohio
Graduate Acceptance Rate: 21.8%
Graduate Engineering Students: 52% International Students
Tuition: $24,532 per year (Full Time)
Minimum TOEFL Score: 92
Minimum IELTS Score: 6.5
Visit for more information – University of Cincinnati Admissions
University of Utah
Type: Public
Location: Salt Lake City, Utah
Graduate Acceptance Rate: 40.6%
Tuition: $18,774 per year (Full Time)
Minimum TOEFL Score: 100 (This score is minimum required for College of Engineering, for other departments score vary)
Minimum IELTS Score: 7.5 (This score is minimum required for College of Engineering, for other departments score vary)
Visit for more information – University of Utah Admissions
University of Missouri - Columbia
Type: Public
Location: Columbia, Missouri
Graduate Acceptance Rate: 30.4%
Graduate Engineering Students: 53% International Students
Tuition: $9,006 per year (Full Time)
Minimum TOEFL Score: 61
Minimum IELTS Score: 5.5
Visit for more information – University of Missouri, Columbia Admissions
University of North Carolina
Type: Public
Location: Chapel Hill, North Carolina
Graduate Acceptance Rate: 30.8%
Tuition: $26,013 per year (Full Time)
Minimum TOEFL Score: 79
Minimum IELTS Score: 7
Visit for more information – University of North Carolina Admissions
Iowa State University
Type: Public
Location: Ames, Iowa
Graduate Acceptance Rate: 18.0%
Tuition: $21,986 per year (Full Time)
Minimum TOEFL Score: 79
Minimum IELTS Score: 6.5
Visit for more information – Iowa State University Admissions
Baylor University
Type: Private
Location: Waco, Texas
Graduate Acceptance Rate: 30.0%
Tuition: $25,866 per year (Full Time)
Minimum TOEFL Score: 76
Minimum IELTS Score: 6 
Visit for more information – Baylor University Admissions
Brigham Young University
Type: Private
Location: Provo, Utah
Graduate Acceptance Rate: 65.8%
Tuition: $13,000 per year (Full Time)
Minimum TOEFL Score: 85
Minimum IELTS Score: 7
Visit for more information – Brigham Young University Admissions
Dartmouth College (Thayer)
Type: Private
Location: Hanover, New Hampshire
Graduate Acceptance Rate: 18.8%
Graduate Engineering Students: 67% International Students
Tuition: $16,040 per year (Full Time)
Minimum TOEFL Score: 100
Minimum IELTS Score: 7
Visit for more information – Dartmouth College Admissions
Tufts University
Type: Private
Location: Medford, Massachusetts
Graduate Acceptance Rate: 45.2%
Tuition: $48,412 per year (Full Time)
Minimum TOEFL Score: 90
Minimum IELTS Score: 6.5
Visit for more information – Tufts University Admissions
Universities for GRE Score 320-325
Universities for GRE Score 325-330
Universities for GRE Score 330-340
Universities for GRE Score 310-315
Universities for GRE Score 300 to 310
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