"Majority" is one of those funny words in English that can either be singular or plural, depending on the context.
Usually, a prepositional phrase with "of" is simply a modifier, and not part of the subject:
The group of students is smart, not the group (of students) are smart.
"Majority" is similar to other SANAM words (some, all, none, any, many), which are considered pronouns that replace the word in the prepositional phrase. So, when we say "all of the students..." "all" is replacing a plural word, and is thus plural. If we say "all of the stuff," it's singular.
none of the unicorns were invisible --> plural
none of the money was stolen --> singular
"Majority" is even more complicated than that, because there can be subtle differences in meaning. Using the singular emphasizes the totality, whereas the plural emphasizes the individual parts.
Thus,
A majority of voters is opposed to the current policy
and
A majority of voters are opposed to the current policy.
would both be correct, but would just have subtly different meanings. The second would generally be preferred, but the first is not incorrect. Because this is an issue of meaning rather than grammar, it is highly unlikely that the GMAT will ever test it directly - just know that neither one is necessarily wrong.
Usually, "majority" will follow the SANAM guidelines: it will be plural if the word after it is plural, singular if the word after it is singular, or if there is no word after it:
the majority of penguins live in Antarctica --> plural
the majority of his house is underwater --> singular
the majority has voted on the issue --> singular
Does that help?
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education