The committee concluded that the students were having academic problems because they "spent large amounts of time on school sports and too little time studying." To remedy this, the director decided to prohibit all students who were having academic problems from taking part in sports in which they were active. In this way the director believed he could ensure that such students would do well academically. However, just because he is ensuring that the students are no longer spending large amount of time on sports, does not mean that he has ensured that the students spend more time studying. Just because the students no longer spend their time on sports does not guarantee that they will use this saved time on academics.
(A) is incorrect because it is irrelevant to the argument. The argument is concerned with how the director will help those students whose academics are suffering due to their immense time spent playing sports and lack of time spent on studies. We are not concerned with the students who play sports and don't have academic problems. Remember, "some" means "at least one" so (A) is effectively saying that "at least one student who spends time on sports does not have academic problems."
(B) is incorrect because it is not what the director fails to establish. If you do academically well, then you have saved time by not participating in sports. Contrapositive: if they don't save time by not participating in sports, then they won't do well academically. Neither of these statements leads us to concluding that the students will do well academically. Therefore, the director's reasoning is not flawed because he fails to establish this answer choice. The flaw in the argument is that we do not know that prohibiting students who are having academic problems from taking part in sports will result in them "saving time." We need to focus on how the time "saved" from not playing sports will be turned into time spent studying.
(C) is CORRECT because it shows how the director's reasoning is not completely sound. The director fails to establish that the time saved from not playing sports will actually be put towards studying. If the students prohibited from playing sports merely use that time to play video games, then it is false to conclude that the director's prohibition of sports will ensure that such students will do well academically. The issue is two-fold: (1) the large amounts of time spent on school sports and (2) too little time studying; both need to be remedied.
(D) is incorrect because it is irrelevant. If it is the case that students who do well academically do not spend time on sports, then students who do spend time on sports will not do well academically. Neither concludes that students will do well academically. Therefore, the director's reasoning is not flawed because it fails to establish this answer choice.
(E) is incorrect because it is, like (D), irrelevant. The quality of the school's sports program has no affect on the director's reasoning.
Hope that helps! Let me know if you have any other questions.
