The argument here is that a drug purported to shorten bouts of vertigo does not actually do so. The evidence? That during a 3-month shortage of the drug, the duration of patient's bouts of vertigo did not change.
There are two assumptions here that you may have noticed (and perhaps others):
1. That the drug's affect appear or disappear within 3-months. Maybe it takes 5 months for the drug to build up enough presence in one's system to affect a change, and a similar length of time to dissipate.
2. That the average duration of the bouts of vertigo is an accurate measurement -- perhaps there were other factors in the environment that lengthened duration for others?
(A) plays on the issue in #1 above. The argument can be stripped down to:
No change --> Not effective, and (A) provides the contrapositive: Effective --> Change
If we were to negate (A) and state that if the drug were effective we would not see a change, then the argument becomes invalid. The overall efficacy and the change witnessed after a shortage would be "unhooked."
As for the incorrect answers:
(B) is tempting. If provides Change --> Effective, which is the reverse of the contrapositive, and so it does not help us. Put simply, we are interested in the effects of there not being a change, not what happens if there were a change.
(C) may be true -- perhaps 4 months would be a better test. But because a fact is less useful than another does not mean it is not true or useful. A DNA match might be better than a fingerprint, but that doesn't mean that a fingerprint is useless or not enough to convict.
(D) is irrelevant. Even if those other factors are relevant, we don't know that the drug is irrelevant. When we negate (D)--diet or smoking does change the duration of vertigo--it actually bolsters the conclusion that the drug has no effect.
(E) is similarly irrelevant. Whether there are significant factors other than the drug does not affect whether the drug is effective.
#officialexplanation