Dear MT:

You wrote:
> I work for a nonprofit that publishes scientific journals on cancer research. We require spelling and grammar tests of all employment applicants. One test item in grammar is on subject-verb agreement, which goes this way:
>
> “She is one of those songwriters who (like, likes) to compose on the piano.”
>
> Our answer sheet indicates the verb “like” to be the correct answer. Is this accurate, and if not, why isn’t it?
>
> I would appreciate your help on this. Thank you.
>
This is one that can go either way. The pronoun “who” can be singular or plural, and in this case the antecedent is ambiguous. If the “who” stands for “one,” then the verb would be “likes.” If the who stands for “songwriters,” the verb would be “like.” Because the word “songwriters” is closest to the pronoun, generally English speakers would understand that the “who” is taking the place of “songwriters” so that the verb would be “like.” If you were to use the verb “likes,” you would be emphasizing the individual person (she) more than the type of songwriter she is.

Either could be correct; they just have slightly different meanings. If you were to ask for the “best” answer, then it would be “like” for the reason above. If you were to ask for the “correct” answer, either might work. I mention this because most standardized mutiple-choice tests like the SAT always say “best” answer. That gives a little wiggle room in case another answer might work in some instances.