How long should it take to hear back from an interview?

Hello veterans! This week is a short week and I have an interview on Tuesday. I accepted a 3 week file clerk position that starts the following Monday (June 1). Do you think I will hear back before the 3 wk job starts?

This other job is a year long contract as an Admin Assistant and I'd rather do that. I will have my Bachelor's Degree in Business Admin by the time I'm done.

Please tell me what you think and no scam ads!!!
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with any luck you should hear before then but if not accept the other job as it will go better on your c.v
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Actually, you shouldn't be waiting at all. You should ask them at the interview exactly when would be an appropriate time for YOU to call them to find out if they are interested in offering the job to you.

This will not only give you the answer you are seeking, but it will show them how eager you are to get the job!
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I agree with Marco. Don't wait by the time the interview is over they know if they want you in their company or not. Just ask, you could say "will it be okay to call you on Thursday for you decision"? then they will think that you have other options and hopefully not drag their feet. Congrats on getting your Bachelor's Degree