This one is tricky, but I believe the answer is E. Let me attempt to explain.
Let's look at (1) first. There are two possibilities here: A is a truth-teller, or he is a liar. If he is a truth-teller, this creates a contradiction: he states that only one other person is a liar, when we know there are clearly two liars, and a truth-teller would state as such. So this cannot be correct.
If he is a liar, we have to look at both ways this statement could be a lie. The first possibility is that there are other liars BESIDES C, but this cannot be the case, because we know there are only two liars, and we have accounted for both: A and C. The other lie is that C is a truthteller.
SO, from statement (1), we have learned that A is a liar and C is a truthteller, but nothing about B and D. So (1) is insufficient.
Let's look at statement (2). Two possibilities: B is a truthteller, B is a liar. If B is a truthteller, everything works out fine, but we don't yet know if he is. Darn. If him lying creates a NECESSARY contradiction, then (2) is sufficient, but a quick glance shows that it does not; B would obviously HAVE to be lying, because there is more than one truth-teller. So (2) is not sufficient. The only two answers left are C) and E).
Since C) Requires BOTH (1) and (2) to be used in conjunction, let us apply what we have learned from (1) to the second statement. If B is the truth-teller, what he says is true, and there is no contradiction. If B is the liar, he is lying in that both C and D are truth-tellers. Since both of these scenarios work out, there is no way to know even from both statements, and thus the answer is E.
Not totally positive here, but that's my best shot. It's a hell of a logic puzzle for a two-minute limit, too.
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