They do look at your employment history. You could mention that you just started a new job but have worked consistently and at other jobs and bring your resume to the interview for the apartment. If they see that you're not job to job and can't hold on to one things may be fine.
The second most important thing is to be honest in your interview and give the impression that you are very responsible. We always tried to weed out people we thought were irresponsible, possible addicts and or potential problems that could irritate neighbors and try to see if they have issues with police and prior landlords. You need references.
I will be honest most people renting out apartments tend not to want to rent to young people. Make sure you present well at the interview and that they gain the right perception of you. That and as I said above a credit check is what can seal fate either way. [ solidadvice4teens's advice column | Ask solidadvice4teens A Question ]
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