Choice "C" is correct. A distributed (or decentralized) processing environment would be the most beneficial when large volumes of data are generated at many (remote) locations and fast access to the data is required. In centralized processing, there is always some delay (however small these days) in transmitting large volumes of data or transactions to the central site to be processed and then to be able to access the processed information. Decentralized processing eliminates that particular problem (although it does present other problems). Note that there seems to be an implied assumption in this question that the (remote) locations need access only to their own local data and not to all of the data for all locations. This choice seems to be better than choice "d". Choice "b" is incorrect. If large volumes of data are generated centrally, centralized processing would probably be more beneficial, regardless of whether or not fast access to that data is required. This choice implies that little, if any, data or transactions are generated at the remote locations so there would be no real need for distributed processing.Choice "d" is incorrect. If summaries of the data are needed "promptly" at the central site, centralized processing MIGHT be more beneficial. Since only small volumes of data are generated at the remote locations, there would probably not be much delay in transmitting that data to the central location and probably not much delay in accessing that data. Since only summaries of the data are needed at the central location, those summaries could probably be readily prepared at the remote locations. This choice is the next best, and a case could certainly be made that the choice is correct. The decision could readily come down to summaries of "what" data. Is it summaries of all of the data generated by all locations or summaries of only the data generated by the remote location? If the former is what is meant, centralized processing would be more beneficial. If the latter is what is meant, distributed processing would probably be more beneficial.Choice "a" is incorrect. If summaries of the data are needed "monthly" at the remote sites, centralized processing MIGHT be more beneficial. However, there is no way to tell in this choice how much data is generated at the remote locations. From the way the question in total is written, an assumption might be made that there is only a small volume of data at the remote locations. If there is a large volume of data at the remote locations, decentralized processing might be more beneficial because fast access is required.
Note: This question is rather vague and ambiguous. Candidates should not have to make too many assumptions or read too much into the question. Unfortunately, with this question, you do.