The question tells us that 7/8 of the students play a sport in the fall semester, so we know that 1/8 of the students do NOT play a sport in the fall.
Statement 1 gives us the number of students who play a sport in the spring semester, but it tells us nothing about the total number of students or the number of students who play a sport in both semesters. Thus, we cannot say what fraction of students play a sport in neither semester. Statement 1 is NOT sufficient. Eliminate answers choices A and D. The correct answer choice must be B, C, or E.
Statement 2 gives us specific information about the number of students who do not play a sport in either semester. In particular, we learn that of the students who do not play a sport in the fall (1/8 of the total), 2/7 do not play a sport in the spring. The fraction of students who play a sport in neither season is the product of these two fractions. Statement 2 gives us enough information to answer the question.
Answer choice B is correct.
Although it is not necessary to solve for the exact fraction on the exam, we will do so for the purposes of illustration. The fraction of students who play a sport in neither semester is 2/7 of 1/8, or (2/7)*(1/8) = 2/56 = 1/28. Therefore, 1/28 of the students play a sport in neither the fall nor the spring semester.
Regards,
Karthik
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