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Sir,

She ran two miles at most.

what is function of "at most" in this sentence?

thanks.
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It means, "the farthest she ran was two miles". It's used to make the suggestion that someone is not being completely honest.

Carol: I ran three miles.

B: [to C] She's full of it. She ran, at most, two miles.
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It's a prepositional phrase, and it quantifies "two miles".