Can you enroll in the Army ROTC at the age of 31 NON-scholarship?

Http://www.hofstra.edu/Academics/Colleges/Hclas/MILSCI/milsci_about.html

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Maybe, but why? You can't ever commission in any service because of age.

Did you miss the part that said "Age requirement: Maximum 34 years of age for non-scholarships"?

You could enroll in the first two years of ROTC as there's no military obligation. However, you would be blocked from the last two years since those years are for future commissioned officers and your age would disqualify you.