Australia is one of the countries that have imposed sanctions on Iran.
(A) one of the countries that have imposed sanctions on --> correct
(B) one of the countries that has imposed sanctions against -->"that" modifies "countries", so "have" should be used
(C) one of the countries which have imposed sanctions on --> need essential modifier "that"
(D) one of the countries which has imposed sanctions on --> same as C
(E) one of the countries that have imposed sanctions against -->"impose A on B" is the correct idiom

The answer is A.

This question does test a rule that comes up a decent bit on the GMAT.

When is one of the Xs singular?
When is one of the Xs plural?
The difference comes down to the presence or absence of these words: THAT/WHO

• RULE: one of the Xs: singular or plural?*

ONE OF THE Xs + THAT/WHO + verb = PLURAL

ONE OF THE Xs + [NO THAT or NO WHO] + verb = SINGULAR

In other words, check for the presence of the words that or who.

See my full post about the rule that governs whether the phrase one of the Xs is plural or singular, with examples, HERE
and Ron Purewal's post HERE.

In this question,
One of the Xs + THAT + verb = plural

An essential modifier should be introduced with that (and without commas, though commas are not an issue in this case).
An essential modifier should not be introduced with which.

And the idiom is sanctions on.


*If the sentence or phrase begins with "The ONLY one (of the Xs)," then the subject is singular.
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Better if you guys explain why you eliminated each answer as opposed to stating "correct".

Here:
Australia is one of the countries that have imposed sanctions on Iran.
(A) one of the countries that have imposed sanctions on
A is correct because the finite verb "have", contained within the relative clause, agrees with the subject "countries", and the correct idiom, "sanctions on", is used.

(B) one of the countries that has imposed sanctions against
Error 1 - Singular "has" does not agree with plural "countries"
Error 2 - The correct idiom is "sanctions on"

(C) one of the countries which have imposed sanctions on
Error 1 - Modifier "Which" must be preceded by a preposition or a comma
Error 2 - restrictive 'that' is more sensible as the info contained in the relative clause is essential to the sentence meaning

(D) one of the countries which has imposed sanctions on
Same as (C)

(E) one of the countries that have imposed sanctions against
Error 1 - The correct idiom is "sanctions on"
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The OA should be A.
That acts like a reset button indicating that a new subject verb pair follows. Here That refers to countries, which will take a plural verb - have. Also, since we are referring to a perticular set of countries we will have to use essential modifier ‘that’ instead of which.

Posted from my mobile device

Official Explanation:

Answer: A

(A) The correct answer. The plural subject countries agrees with the plural verb have, and the correct idiom is sanctions on.

(B) Singular has does not agree with plural countries. The correct idiom is sanctions on.

(C) The use of which is incorrect.

(D) The use of which is incorrect.

(E) The correct idiom is sanctions on.
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(A) one of the countries that have imposed sanctions on -- Fixes the error in other options. Correct.
(B) one of the countries that has imposed sanctions against -- SV error. One of the Xs + That + verb is PLURAL.
(C) one of the countries which have imposed sanctions on -- "which" must be preceded by a comma and "which" is to bring out non essential info. Not the case here.
(D) one of the countries which has imposed sanctions on -- Same as B.
(E) one of the countries that have imposed sanctions against -- Incorrect idiom.