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I scored a 139 on a practice test, I know terrible, but I was up until 4am the night before and I was absolutely exhausted half-way through the exam. Prior to taking that practice test, I'd done no type of preparation. So my question is, honestly, is it unreasonable to think that I could score a 162-166 with sufficient test prep?

It depends on what you define as "sufficient prep". However, in general I think anyone can score above a 160, even above a 165 if you really truly work your ass off. However, I want to emphasize work hard. You may need a solid 6 months to get up there, but its definitely possible if you keep at it and are smart with your study methods.

Can you do it? Most likely.
Will it require more work than you think? Most likely.