Will sending apps a month after opening have a large effect?

[sixpence]

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I'm trying to choose my mcat date. Taking it in end of may would mean I could send in my app at best the end of June. So I'm wondering how big is the difference between applying June 1st and four or so weeks later. Also, I'm applying to mainly texas schools, so what effect does that have on what "early" is? My stats/app isn't that great so I know I need to get it in the earliest possible to make up for whatever I'm lacking. At some texas schools i think the first interview date is the end of july. Would I be considered for that only if I send in my app the day it opens? Thanks!