Data Sufficiency

7/8 of the students at Edgemont High play a sport in the fall semester. What fraction of the students play a sport in neither the fall nor the spring semester?


1. 280 students play a sport in the spring semester.
2. 2/7 of the students who do not play a sport in the fall semester do not play a sport in the spring semester.

Let total students be x

7x/8 play in the fall semester, which means x/8 don't play in fall

x = Fall only + Spring only + both fall and spring + neither fall and spring

1)

x = 7x/8 + Spring only + neither => spring only + neither = x/8

Not enough to find neither

2)

> 2/7 of the students who do not play a sport in the fall semester do not play a sport in the spring semester

(2/7) x (x/8) = x/28 do not play in the spring semester, and neither do they play in the fall semester.

Since total number of students = x, we can find the ratio (1/28)

Hence (B)

OA pls?

I think it is B.
I don't have the OA

OA is B

B!

sanyalpritish wrote:7/8 of the students at Edgemont High play a sport in the fall semester. What fraction of the students play a sport in neither the fall nor the spring semester?


1. 280 students play a sport in the spring semester.
2. 2/7 of the students who do not play a sport in the fall semester do not play a sport in the spring semester.

B It is!

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.