Will you/won't you?

Help yourself to a drink, _________?

A. Will you

B. Won't you

So, according to the answer sheet, B is the answer because the question is in fact an offer made to someone and B is more polite. Does that make A incorrect? What about "would"? That can fit in the sentence too. What difference do these 3 make in the meaning? Plus, is B really more polite? It seems kind of frustrated to me.

Thank you.

Well, either is grammatically correct, but they have different meanings.

When using question tags, we use the negative form of what we want/mean. According to this eslbase.com page:

If the auxiliary verb in the sentence is affirmative, the tag is negative.

You’re Spanish, aren’t you?

If the auxiliary verb in the sentence is negative, the tag is affirmative.

You’re not Spanish, are you?

So, "Help yourself to a drink, won't you?" implies the opposite: you should help yourself to a drink. It is therefore a polite offer.

"Help yourself to a drink, will you?" implies the opposite: you shouldn't help yourself to a drink. It might be used in situations such as someone random walking into a private party, and taking a drink. It might be followed up with some aggressive behaviour by the person who said it to the person who took the drink.

Just to make it confusing, I've thought of another meaning of "Help yourself to a drink, will you?". It could be used when the speaker is frustrated that somebody hasn't done something already. It would usually have the word "just" at the beginning:

Just help yourself to a drink, will you?

I can't think of any grammatical "rule" for this usage. But it certainly isn't a polite offer. In speech you could tell this apart from the "aggressive / you shouldn't have done that" meaning above by the stress, emphasis and speech pattern/timing. I can't work out how to make that clear in writing, as the "will" will be stressed in both versions. In writing the context should make it clear which is used.