See, the argument states that "a course of treatment with an antibiotic often gives rise to antibiotic resistant bacteria, since the bacteria that survive a given antibiotic are the ones most resistant to it, and they are the only ones left to replicate.
The underlined portion means that "continuous" use of an antibiotic will give rise to a bacteria that would be resistant to this "particular" antibiotic. Now, if I periodically change the type of Antibiotic, than I can prevent the growth of the bacteria as they grow due to continuous use of a particular antibiotic.
The ans should be C