No flaw. (A) establishes a conditional relationship with two separate sufficient conditions: If the inhabitants were invaded or the climate changed, then the architecture would have changed. It then validly concludes that the absence of the necessary condition (changes in architecture) means that one of the sufficient conditions is missing (the inhabitants being invaded).

Wrong flaw. (B) attempts to give us a conditional relationship (if the opposition party cuts wages, then workers will strike), but it only tells us that people think this will happen. As such, no conclusions can be drawn using this statement. The stimulus, meanwhile, makes an invalid conclusion based on a conditional statement with a conjunction in the sufficient condition, so (B) doesn’t match.

(C) establishes a conditional relationship with a conjunction in the sufficient condition: If a company sold its subsidiaries and purchased a new patent, its stock price would have doubled. It then concludes that a specific part of the sufficient condition is absent because the necessary condition is absent. The stimulus also concludes that a specific part of the sufficient condition is absent because the necessary condition is absent, so (C) matches.

Wrong flaw. (D) establishes a conditional relationship: if the rebels won and the leaders were freed, then residents were expected to show support. It then concludes that the presence of the necessary condition implies the presence of part of the sufficient condition. The stimulus, however, concludes that the absence of the necessary condition leads to the absence of part of the sufficient condition, so (D) doesn’t match.

Wrong flaw. (E) gives us a conditional statement with two separate necessary conditions: if the equipment was worth it, then both the accuracy of forecasts and ratings would have increased. It then concludes that the absence of one of the necessary conditions means that the new equipment is not better than the old equipment. This is different from not being worth the investment, so this conclusion is flawed. The stimulus, however, presents a conditional relationship with two parts to the sufficient condition, so (E) doesn’t match.