The correct option is C If a person has an IQ of 130 and is attending an Ivy-League school, it is possible for him or her to have graduated from TopNotch High School.
(A) The passage states that every student with an IQ of 150 who applies to the Ivy League will be accepted by at least one of the universities. However, it is possible that a graduate of TopNotch High with an IQ of 150 did not apply, and thereby was not accepted, to any of the schools. Hence, this conclusion is not valid.
(B) The passage states that every graduate of TopNotch High has an IQ of over 120. The conclusion only states that the student is a high school graduate and that he has an IQ of less than 120. It does NOT state that he or she was a graduate of TopNotch High. It is possible, however, that after attending TopNotch High for a period of time, he or she graduated from another high school. If this is the case, the situation does not contradict the passage, but contradicts the conclusion (he or she was a student at TopNotch High). Hence, this conclusion is not valid.
(C) Nothing in the passage precludes a person who is a graduate of TopNotch High from having an IQ of 130 and from attending an Ivy League university. Neither does anything in the passage preclude a person who has an IQ of 130 and is attending an Ivy League school to have graduated from TopNotch High. Therefore, it is possible for both situations to exist simultaneously, so the conclusion is valid.
(D) The conclusion states that most, but not necessarily all, of the graduates from TopNotch High with IQ of 120 who apply to the Ivy League are accepted by at least one of the school. The conclusion, however, does not state positively that any of the TopNotch High graduates had an IQ of over 150. Hence, even if it is unlikely, it is possible that none of the TopNotch graduates had IQ of over 150, and, of the remaining graduates who applied to the Ivy League, none were accepted to an Ivy League university. This conclusion is thereby not valid.
(E) The passage states that any student with an IQ of 150 who applies to one or more Ivy League universities will be accepted to at least one of them. It is possible, however, that some of those who had applied and been accepted to an Ivy League university chose not to attend. Hence, this conclusion is not valid.