didn't happen since

Question

Tom says: My God, Jeff, you have lost a lot of weight!

Jeff replies: Twenty pounds! New Year's resolution.

Tom says:

a. You can't have lost twenty pounds since New Year's. You must have started dieting before.

b. You haven't lost twenty pounds since New Year's. You must have started dieting before.

c. You didn't lose twenty pounds since New Year's. You must have started dieting before.

Are the sentences a-c grammatically correct and can they be used in this context?

The idea is that all this change couldn't have happened in such a short time and therefore the process of losing weight began before New Year's.

Many thanks

Answer 1

Yes, these are all grammatically correct, although it's worth noting they have slightly different meanings.

"Can't" in this context implies that it is impossible, but that you have no specific knowledge of his diet, just dieting in general.

The second one and third one's imply that you have prior knowledge, such as having seen Tom on New Year's, but it is only weakly implied.