AmoyV
The vendor informed the company that
neither of their orders were ready.A. neither of their orders were ready
B. neither of its orders were ready
C. neither of its order was ready
D. neither of its orders was ready
E. its orders, neither of them, were ready
Dear
AmoyV,
I'm happy to help.

This SC question is not entirely GMAT-like, because it's so anemic, but its logic is sound.
The word "
neither" is ALWAYS SINGULAR. See:
https://magoosh.com/gmat/2013/gmat-sente ... agreement/Thus, we need a singular verb with "
neither."
This question also contains a classic pronoun trap. The word "
company" is singular --- yes, there may be several people who work there, but the word itself is singular, and requires a singular pronoun, "
its", not "
their." See:
https://magoosh.com/gmat/2013/gmat-pronoun-traps/Choice
(A) is out because of the pronoun mistake, and both choices
(A) &
(B) are out because of the verb mistake. There are two orders, so the word "orders" must be in the plural, so
(C) is wrong. Choice
(E) is embarrassingly wordy and indirect, a nightmare: this is wrong. This only leave
(D), which is perfectly correct on all counts.
Does all this make sense?
Mike