Teachers tell students that sentences with few should take positive question tags, but this is an over-simplification and is not always true.
Few and little are among the words that are approximate negators. When these words are determiners within a noun phrase before the verb, they make the clause negative, so a positive tag is used. This does not work with a few and a little, which are positive. It also does not work with the comparatives and superlatives fewer, fewest, littler, least.
So the following are acceptable:
(1a) Few people drive Jaguars, do they?
(1b) A few people drive Jaguars, don’t they?
(2a) Few of the students did well in the German exam, did they?
(2b) A few of the students did well in the German exam, didn’t they?
(3a) Little ketchup is left in the bottle, is it?
(3b) A little ketchup is left in the bottle, isn’t it?
When these approximate negators occur late in the clause, the results of polarity tests (that is, whether the clause is positive or negative) are less clear. For many speakers, including myself, the tag had he? is at best only marginally acceptable in the following sentence (quoted from Huddleston & Pullum, page 820):
(4) He had so far shown the visitors few of the sights of London.
Even in a short sentence that has few in the object, I find a positive tag to be questionably acceptable. I would much rather put a fixed tag such as right? or isn’t that so?
(5a) ?Ahab has few friends, does he?
(5b) Ahab has few friends, right?
Few and little can also be used as a modifier with a definite determiner. In this case, they do not mark the clause as negative and a negative tag is used.
(6a) Few teachers attended the conference, did they? (few is a determiner; the clause is negative and the tag is positive)
(6b) The few teachers who attended the conference thought it was very useful, didn’t they? (few is a modifier; the clause is positive and the tag is negative)
Other definite determiners are these, those, and possessive pronouns (my, your, his, her, its, our, their).
I am not suggesting that students should be taught all these distinctions, as they are beyond the syllabus. I am suggesting that teachers and exam setters should limit the sentences they present to students for tags to the types shown in (1-3). Teachers have a tendency to over-simplify the rules and then they or their students produce ungrammatical sentences.
Source: Rodney Huddleston & Geoffrey K. Pullum, The Cambridge Grammar of the English Language, Cambridge University Press, 2002, pages 394, 815-820.