Data Sufficiency

jjjinapinch wrote:Last school year, each of the 200 students at a certain high school attended the school for the entire year. If there were 8 cultural performances at the school during the last school year, what was the average (arithmetic mean) number of students attending each cultural performance?
(1) Last school year, each student attending at least one cultural performance
(2) Last school year, the average number of cultural performance attended per student was 4.

We are given that there are 200 students and 8 cultural performances. We need to determine the average number of students attending each cultural performance. Thus, we need to know the total attendance of the 8 performances. For example, if we know the total attendance of the 8 performances is 1,000, then the average number of students per performance is 1,000/8 = 125.

Statement One Alone:

Last school year, each student attended at least one cultural performance.

Although we know that each student attended at least one cultural performance, we do not know the total attendance at the 8 performances, and thus we cannot determine the average number of students per performance. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

Last school year, the average number of cultural performance attended per student was 4.

Since the average number of cultural performances per student was 4 and there were 200 students, the total attendance at the 8 performances was 200 x 4 = 800, and thus the average number of students per performance was 800/8 = 100.

Answer: B

olilondon wrote:Hi!
How do you know in S2 that all the 200 students attended at least one performance? It would have been different if from the average of 4, the student attended to at least one performance were 100, thus (4)(100)=400. 400/8= 50.
You need S1 to confirm the number of attendees that at least participated from 1 cultural performance.
Thanks in advance.

Hi olilondon,

The initial data in the prompt tells us that there are 200 students in the school and 8 performances. The information in Fact 2 tells us that the average number of performances attended PER STUDENT (meaning "per student in the school") was 4. By extension, that means that total number of student-attendances was (200)(4) = 800. Regardless of whether 100 students attended 8 performances each, 200 students attended 4 performances each, etc., the average number of attendees PER EVENT would be 800/8 = 100. Thus, Fact 2 is sufficient.

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