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I will be taking the September LSAT in which I will most Linley get a 173 and get my results back by the beginning of Oct and apply as soon as I get the LSAT score back which would be two weeks after the HLS app opens up. I have a 3.91 gpa, good rec letters, and average ECs.

Would applying at the beginning of Oct. hurt my chances significantly when compared to applying the day of?

If so would it be good or bad to take the June LSAT as well and send in an application with a lower LSAT score and then resubmit in October?
Thanks!

Are you talking about taking next year's September LSAT? Because you can't take the June LSAT anymore.

Anyway, in order:

-Don't count your LSAT scores before they hatch.
-Literally no difference between applying in September and October.
-Stop focusing on Harvard because of prestige.
-Relax.