The way I read the question, it says
Cecily will not
appoint anyone without explicit consent. But note that she can
reject anyone without any consent.
Now Steve and Joanne don't speak with each other, so they can't provide consent together.
And either will not provide consent unless he knows whether the other person is admitted. So there is no chance that both can provide consent and be appointed.
But Cecily can reject either one of them and then the other can provide consent and be admitted.Lets take the case if Cecily 1st goes to Steve to get his consent and Steve wants to know will Joanne be admitted. Since Cecily doesn't have a consent from Joanne, she can't admit Joanne, but she can reject Joanne and then Steve will have no problem in providing a consent and joining the committee.
Similarly Cecily can reject Steve, get consent from Joanne and admit him. But she will never be able to admit both Steve and Joanne as it is a deadlock situation.
Hence
E is the correct option. E) Either one of them can be appointed, but not both.