Mismatched conclusion. (A) has a conditional statement, but concludes that the absence of the sufficient condition will lead to the absence of the necessary condition. This is a flawed reading of the statement, so (A) doesn’t match.

The argument proceeds by presenting a conditional statement (If Peter didn’t buy a house, he would have rented an apartment). It then validly concludes that the absence of the necessary condition implies the absence of the sufficient condition.

Mismatched premises and conclusion. (C) presents a conditional statement (if Linus’s car is not working, then Renate will drive him to work), but this is merely a promise Renate has made, and we don’t know if she will uphold her promise. (C) is also attempting to go from the sufficient condition to the necessary condition, whereas the stimulus uses the contrapositive.

Mismatched conclusion. (D) presents a conditional statement (if TV not working, then movie), but it attempts to read the statement by going from the sufficient condition to the necessary condition. We’re looking for the contrapositive, however, so (D) doesn’t match.

Mismatched conclusion. (E) has a conditional statement, but concludes that the absence of the sufficient condition led to the absence of the necessary condition, which is flawed. We also can’t conclude that someone else solved the problem, as it may have simply remained unsolved. We’re looking for a valid argument, so (E) doesn’t match.