Each of the factory towns which has pollution as a severe problem is

Got it right: B

(A) which has pollution as a severe problem is >> 'which' refers to towns (plural), so 'has' is wrong.
(B) where the pollution problem has become severe is >> correctly refers to 'towns'
(C) where the pollution problem has become severe are >> "each" is singular so 'are' is wrong
(D) in an area in which the pollution problem has become severe are >> wrong 'are'
(E) in which the pollution problem has become severe are >> wrong 'are'

Can you please clarify how does "which" refer to plural? Or if the first option had " which have" then would it be the correct choice? Please reply. Thanks in advance

Yes your analysis is correct.

If option A had had have instead of has then it would have been one strong contender to OA, but I would still prefer to use where rather than which because where suits to modify a place such as town.

Further, for your first question : Can you please clarify how does "which" refer to plural?
I would say this is one of the signature format of GMAT; some official questions were created to test this logic and further other prep companies also created their own versions. Refer following sentence.

Lake Michigan, one of the lakes that flow through United States, is the largest fresh water source.

... one of plural that verb(plural) ...
... one of plural, which verb(plural) ...

Refer this question and explanation as well :
twenty-two-feet-long-and-10-feet-in-diameter-the-am-1-is-12821-20.html#p1381818
Note it down in your error log.

Thanks a lot Piyush for the explanation. But I am still unable to internalize this plural usage. I have always thought that "Each of " and "One of" should be singular.

I think you are mixing two concepts. Refer following sentences.

Each of these shirts is nice. -- here subject is each ... so we used singular verb.
Each of these shirts, which were hanging on display, is nice. -- here relative pronoun which is referring to the shirts. Therefore, subject of relative clause is plural shirts and we need a plural verb inside relative clause. Further you can see main verb is still singular.

one of ... is special in this aspect as there is no exception to construction as recommended in my previous comment.

KAPLAN OFFICIAL EXPLANATION:

B

Let's start by deciding whether the verb at the end of the underlined section should be “is”or “are.”What is the subject of the verb? “Each of the factory towns.” Since “each” is always singular, the correct verb form must be “is”; this narrows our choices down to (A) and (B).“Which has pollution as a severe problem” is awkward and “where the solution problem is severe” is not, so (B) is the correct answer.

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