Q: "The sale goes on [...] the 16th."
a. through (correct)
I really don't understand why through is the answer.
Context note: This is a practice question from TOEIC.
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ODO on through sense 4:
[preposition] North American up to and including (a particular point in an ordered sequence):
they will be in London from March 24 through May 7
None of the others make sense at all [although this use of through is not used in British English].