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Can I buy an out of the money call and then sell it before the strike price?

I'm 18 and new to options trading so if this question does not make sense or is stupidly easy please bear with me. I'll try to show my thought process through an example.

Ex. I buy a deep out of the money contract of XYZ at a strike price of $120 for $.06 (.06*100)= $6 which is currently trading at $100 with 3 weeks left until expiration. If XYZ shoots up to $115 the next week will I be able to "sell" my contract back for a profit (say premium is now $.12)? Or can I not sell an OTM contract until it is ITM? Thanks I appreciate any response.