Question Tag for "Each"

Each of the students has done well in the examination, hasn't he? Is this correct question tag or it should be "haven't they"?

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?