if subjects (X and Y) are placed in Either X or Y type of construction then the closest subject decides the singular or plural form of verb.
Every Monday,
either the math department chair or the members of the department posts a challenge problem to the student body, but usually it is so difficult that they cannot solve it in a week’s time.
(A) either the math department chair or
the members of the department posts a challenge problem to the student body, but usually it is so difficult that they
(B) either the math department chair or
the members of the department post a challenge problem to the student body, but usually the problem is so difficult that the students
(C) either the math department chair or
the members of the department posts a challenge problem to the student body, but usually the problem is so difficult that they
(D) either the members of the math department or
the department chair posts a challenge problem to the student body, but usually it is so difficult that
they(E) either the members of the math department or
the department chair post a challenge problem to the student body, but usually the problem is so difficult that the students