Choice "C" is correct. In this question, a new "retail" location is being opened. Retail locations will normally have a large number of small transactions (think of a convenience store selling beer and chips), and that might make batch processing look to be most appropriate. However, it is important to know the current status of inventory so that inventory (what is and what is not selling) can be properly replenished (think of Walmart and its supply chain systems) and so that quick price reductions can be made for inventory that is not selling. This last factor makes real-time processing most appropriate.
Choice "a" is incorrect. There is nothing wrong with batch processing, but batch processing would probably not be used these days in the situation described in the question. In the past, batch processing was used to upload transaction data from individual stores to the retailer's centralized processors (with the remainder of the processing being done centrally and possibly in batch); however, real time processing would be better (and more expensive). This kind of decision is almost always a cost/benefit decision. It would certainly be possible, in this situation, to have the retail store transactions uploaded after the close of business in batch, further processing of the transactions to be done centrally in batch, and new inventory figures transmitted back to the store in batch after the central processing is complete.
Choice "d" is incorrect. Sequential file processing is almost totally restricted to batch processing. Before direct access media were available at a reasonable cost, sequential file processing was used extensively. Tapes (which are commonly used for sequential files) are normally restricted to backups and storage for very large amounts of data that are too expensive to be stored on disk and for which there is no real need for relatively quick access.
Choice "b" is incorrect. Direct access processing is not a term used to describe a processing method. Direct access refers to the method of accessing data on a storage medium. Direct access means that you can go directly to a location on a storage device without reading through all of the data as would be necessary in sequential access.