Target question: What was the average (arithmetic mean) number of students attending each cultural performance?

Given: 200 students. 8 cultural performances

Statement 1: Last school year, each student attending at least one cultural performance
There are several scenarios that satisfy statement 1. Here are two:
Case a: every student attended exactly 1 performance last year. So, the TOTAL attendance was 200 last year, which means the average number of attendees for each performance = 200/8 = 25
Case b: every student attended exactly 2 performances last year. So, the TOTAL attendance was 400 last year, which means the average number of attendees for each performance = 400/8 = 50
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Last school year, the average number of cultural performance attended per student was 4.
So, the TOTAL attendance was last year = (200)(4) = 800
This means the average number of attendees for each performance = 800/8 = 100
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer:

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(1) If each student attended at least one performance, then 200 students attended at least one of the 8 performances..But we cannot deduce the number of students who attended all the 8 performances..Not sufficient

(2) The average number of cultural performances attended per student is 4..Hence total performances attended by 200 students will be 800..But we cannot deduce the number of students who attended all 8 performance

Think 100 students 1 performance and 100 students 7 performance
Think 50 students 2 performance, 50 students 4 performance and 100 students 5 performance

Hence E
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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
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Hi

Yes, statement 2 doesnt tell us whether all 200 students attended or not. But lets look at what we need to know. We need average no of students attending each performance. So we need = (total attendance in all performances combined)/(no of performances).

Statement 2 tells us that total attendance was 200*4 = 800. And denominator (no of performances) is given 8 anyway. So our question can be answered.

I am not able to get my head around statement # 2 and how it is sufficient to answer the prompt question.

Statement 2 tells us: Last school year, the average number of cultural performance attended per student was 4.

My interpretation of the above:
Given: [(# of events attended by student 1) + (# of events attended by student 2) + ....(# of events attended by student 200)]/200 = 4
Follows, [(# of events attended by student 1) + (# of events attended by student 2) + ....(# of events attended by student 200)] = 800

800 is, then, the [sum of # of events attended by all 200 students] and the question asks us about average attendance which is [sum of attendances in all events]/8. aren't the two items in the square brackets quantities of two different things? How can they be seen as the same in order to arrive at the conclusion this statement is enough?

Any help is greatly appreciated!

Hi VQ,

You do have the correct answer, but you've made a slight 'interpretational error' in how you worked through the prompt. We're asked for the average number of student attendees at the 8 cultural performances that year. Thus, to answer this question, we need to know the total number of students who attended those 8 shows (either the 8 individual numbers or the overall sum of them); then we can divide by 8 and we'll have the answer.

With Fact 1, we know that each student attended AT LEAST 1 of the performances, so that's 200 attendees at the minimum. This tells us that the average was AT LEAST 200/8 = 25 attendees per performance, but we don't have the exact number (so Fact 1 is Insufficient).

With Fact 2, we know the average number of visits PER STUDENT, so we can determine that there were (200)(4) = 800 total student attendees for the 8 events. Thus, we know that there were exactly 800/8 = 100 attendees, on average, for the 8 events (and Fact 2 is Sufficient).

GMAT assassins aren't born, they're made,
Rich
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What a sweet explanation. Kudo for you.
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