Do schools often start reviewing your app before LOR come in?

[subdermallight]

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I hear mixed things on this. Some schools of mine have been waiting on a letter (nice to have but not essential) and I'm wondering if I should just drop it so that I can be "complete". Letter will be in by Thursday according to my writer. At what point, given the lateness in the cycle, should I definitely drop this letter?

Edit: Secondary already submitted, to clarify