You may come if you like, but you __________. A) don't haveC) don't needB) needn'tD) mustn't
I know answer B is correct, but is wrong with answers A and C? Should they have been "don't have to" and "don't need to"?
This is tricky. 'Need' is only a marginal member of the auxiliary verbs. In fact it makes a difference whether it's positive or negative:
You need go.
You needn't go.
So, as 'needn't' can be an auxiliary, we can say 'but you needn't'. (You can't say 'But you need'.) As an auxiliary, it is followed directly by the plain verb ('go').
As an ordinary (non-auxiliary) verb, 'need' and 'have' take a following 'to' before the next verb. This means that in truncated contexts they need the 'to': I need to; I have to. So you can't say 'but I need' or 'but I have' in your sentence - they're not true auxiliaries so you need the 'to' at the end.