none - singular or plural

IMO, "NONE" is both - Singular as well as Plural. It depends on how it is used.
However, there is also a differential view which says that None is singular only.

Generally,
Wherever the meaning is "Not One" it is singular; and
Wherever the meaning is "Not Any" it is plural.

I would suggest you to go through following BTG post on the same topic.
One of the GMAT experts have answered it stating that such questions are normally not asked in the GMAT.

Hope this helps.

https://www.beatthegmat.com/none-of-plur ... 28799.html

None can be used in singular as well as plural forms. On the contrary, none usually takes singular forms! But both are valid depending on the sentences.

Depends on the usage. When none refers to "not one" or "no part" then it takes a singular form. However when none is used to refer to "not any" it takes a plural form.

For example:

None of the ballplayers were on the team bus after the game. (Here none refers to not any of the ballplayers so none takes a plural form).

None of the apple was eaten. (Here none implies no part). It should be noted that on the GMAT this construction is extremely rare. I can't say whether its totally absent, that's for experts to tell you.