This question is from GRE Practice Problems. The explanation the book has is:
6. (C). The exterminator explains the effects of using poisoned food to combat a mouse infestation: mice will pick up the food an carry it to the nest, where all of the mice will eat the food and die as a result. The exterminator then claims that if X happens, then it will be certain that Y happened first. Specifically, he claims that if all signs of the mice disappear for three consecutive weeks after setting out poisoned food, then the mice all must have died as a result of that poisoned food. The correct answer will weaken this claim, for instance by showing that if X happens, it will not necessarily mean that Y happened; perhaps there is another reason why happens.
(A): this choice is very tempting, but the exterminator argues that "all signs" of the mice "disappear"; this choice mentions only the difficulty of seeing and hearing mice. These do not represent "all signs" of an infestation; mice may leave dropping, chew things up, and so forth. Further, the mice are not harder to see and hear only after poison has been used. They are always hard to see and hear, so this does not provide an alternative explanation as to why signs might diminish or disappear after poison has been used.
(B): this choice may be true, but it does not address the exterminator's claim that if all signs disappear, then the poison must have killed the mice.
(C): CORRECT. This choice offers an alternative explanation for absence of signs of an infestation. If the mice have left the house, then any signs of infestation would also cease because the mice are no longer there. However, the signs will have ceased because the mice left voluntary, not because they have been eradicated by the poison, as claimed by the exterminator.
(D): it is likely true that different poisons have different levels of efficacy, but this argument does not distinguish between types of poison. The claim is simply that the poison must have killed the mice (as opposed to some other explanation for why the signs of the mice would disappear).
(E): The exterminator does not claim that the poison will work within three weeks (or within any time frame at all). He only claims that if the signs disappear over three consecutive weeks, then that means that the poison worked. It might be the case that the signs don't disappear until weeks 3, 4, or 5, but the exterminator's claim would still hold: because the signs have disappeared for three consecutive weeks, the poison worked.