Question Tag for "Each"

I have referred to the Word Master which treated "each of the girls " as singular and the example given is " each of the girls was given a prize" Then I referred to Oxford's Advanced Dictionary which says " each means one or more than two treated separately.The example given is "each of them went to the park" which does not indicate whether the subject is singular or plural

I have referred to Michael Swan's Practical English Usage which says that "which" is normally treated as singular which implies that each may some times be treated as plural as Mr Hot licks pointed out

So far as my knowledge goes each of the students has done well in the exam , hasn't he? is more puristic than
each of the students have done well in the exam' haven't they? I do not know whether native speakers treat each of the students as singular or plural

Besides, students is neutar gender so things have been comlicated.so I think it depends on the situation .If the students are all girls, the equestion tag may be hasn,t she? if they are boys it is hasn't he? is normal but If the group is mixed I think haven't they? is natural despite the grammatical rules

If the students are from an all-boys school (a single-sex school), then the solution suggested below is acceptable.

Each boy (student) has done well in the examination, hasn't he?

From a grammatical point of view, the purist might suggest the following, but it would sound awkward.

Each one of the students has done well in the exams, hasn't he or she?

If the school is mixed-gender and we want to avoid writing each male and female student, then I would suggest keeping the verb plural even though some purists might snort hootily.

Each one of the students have done well in the exams, haven't they?

From English Grammar Today (Cambridge Dictionary)

When we use each of with a plural noun as subject, it’s normally followed by a singular verb:

Each of the buildings is surrounded by high metal fencing.

Each of the horses has won major international races.

For emphasis, we use each one of with determiners and pronouns. When the phrase each one of is the subject, the verb is singular:

Each one of the passport control desks now has a camera as well as a computer.

 

Each + pronouns and possessives

We use each with plural pronouns and possessives, especially when we don’t want to say he/she, women/men, etc.:

Each person who joins the gym gets a free bag and they get a pass to bring a friend for a free visit.  (Each person and they avoids saying each man and woman and he, she.)

Each member of the community should take pride in their local environment.

So, even though each of refers to a singular subject and takes a singular verb, we can take the "singular they" in tag questions to avoid the scene of a gender discrimination, as in:

Each one of the students has done well in the exams, haven't they?