Good discussion, here's the official explanation:
Princeton Review
The sentence is correct as written.
The underlined portion of the sentence contains the verb were, so check for subject-verb agreement and verb tense errors. The non-underlined portion of the sentence uses the word if to speculate about a hypothetical situation so the subjunctive mood is correct. In the subjunctive construction, the if clause uses the verb were, regardless of the subject. There appears to be no error in the original sentence, so keep choice A. Because there is no error in the original sentence, there are no obvious repeaters to look for, so evaluate the remaining answer choices individually looking for reasons to eliminate each.
Choice B eliminates the phrase at least which changes the meaning of the sentence because it does not allow for the possibility that she might score more than six points higher. Eliminate choice B. Choice C introduces a verb tense error by incorrectly using the verb was in a sentence that requires the subjunctive mood construction, so eliminate choice C. Choice D also introduces a verb tense error by incorrectly using the verb was in a sentence that requires the subjunctive mood construction, so eliminate choice D. Choice E introduces a verb tense error by incorrectly using the past perfect tense verb had been in a sentence that requires the subjunctive mood construction, so eliminate choice E.
As per
MGMAT, this follows the pattern of "IF Hypothetical Subjunctive (Simple Past), THEN Conditional (WOULD+Verb)" except that THEN is omitted and the clauses are switched around:
(THEN) Conditional,
IF Hypothetical Subjunctive.
(THEN) Nicole
would be allowed to choose among the honors, enrichment, and liberal studies programs
IF her score
were at least six points higher.
Takeaway: Memorize that Hypothetical Subjunctive uses the Simple Past for all verbs except for "to be," which uses the WERE form.