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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You may find it easier to interpret the information in this problem if you imagine that each student had to have a ticket whenever he or she wanted to attend a particular performance.

The question is about the average number of tickets per performance:
T/8 = ? , which can be rephrased as T = ?

T: total number of tickets used by students

(1) If each of the 200 students attended at least one performance, then T ≥ 200, which doesn’t give us a unique value for T. Insufficient

(2) This statement tells us that T/200 = 4, which gives us a unique value for T. Sufficient

Answer: B
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(1) We dont know exactly the number of cultural performance each student attends, so we can't calculate the average numbers of students attending each cultural performance. Insufficient.

(2) The average number of cultural performance attended per student was 4, so there are totaly 200*4=800 selections in that school.

Hence, the average selections/students for each cultural performance is 800 / 8 = 100 students. Sufficient.

The answer is B.
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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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Average number of students attending each cultural performance =
(total number of students in all performances)/(total number of performances)

This above is what we need to know.

Statement 1. Each student attended at least one. But with this information, we cant say what was the total number of students in all performances put together. If each attended only one, total will be 200*1 = 200. If each attended three, total would be 200*3 = 600. So we cant say.

Statement 2. Average number of performances attended per student = 4
This tells us that total performance attendance = 200*4 = 800

Thus, average number of students attending each cultural performance =
(total number of students in all performances)/(total number of performances) = 800/8 = 100.
Sufficient to answer our question.

Hence answer is B

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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Dear All,

I'm convinced the answer to this question CANNOT be B because though statement 2 tells us the average number of attendance per student to the cultural show, it doesn't indicate that ALL the 200 students attended. So it seems to me that we are making the assumption here or the statement is allowed to be interpreted with an inherent assumption, I don't see how the answer is B.

Can anyone kindly enlighten me?

Thanks.

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.

In this question, we are supposed to find out average no# of students attending each(individual) show and not average no# of students attending each(all) of the 8 shows. Correct me if I'm wrong?? Bunuel

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!

Prompt is asking for (total attendance)/(total number of performances). Total attendance is the number of students multiplied by cultural performances attended so there can be different scenarios e.g. total 200 can attend all 8, 200 can attend only 4, or 100 can attend only 1. Infact, there is no restriction that all students should attend the performance.
I) tells us that out of 200 students each student attended ≥ 1 performance, the average can be 200/1 = 200 or 200/2 =100 and so on. Clearly Insufficient.
II) gives an average for the performances attended per student i.e. (total attendance)/(total number of students) =4. I know total number of students is 200 so sum i.e. total attendance is 800. I can solve for this. Sufficient.
EMPOWERgmatRichC is my understanding about the total attendance correct? Would really appreciate your feedback. Thanks.

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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It's shame I can give only one kudos to this solution. Feel like giving it a hundred kudos at once.

With about 2mins for a question for the test taker, it's just good to give solutions that simplifies the question and goes straight to the point.

GMAT quant is not an 'I can solve math" contest. It's a test of logic. Very Long solutions are impractical on the test day and doesn't help the test taker in anyway. Bcos the enemy is not the question but TIME is.

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Hai,

I have a doubt about how statement 2 is sufficient.

Considering the statement 2 alone, we are not aware that whether each student attended at least one program.

What if one of the programs is not attended by any of the students?

Then in this case total number of appearances, 200*4 = 800.

800/7.

If two of the programs not attended by any of the students, then 800/6

We are not getting any conclusive results.

If we add statement 1 which says each student attend at least one program, then all the 8 programs are attended by 200 students.

So, we can get 800/8=100 conclusive evidence. Hence the answer is C.

This is my understanding on this question.

Please enlighten me by correcting my mistake.

Bunuel

Hi SaravananA,

This prompt asks us 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 each of 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. Whether an individual student attended any of the shows or not is irrelevant, since we're told that there are 200 students in the school and we're asked for the average attendance PER PERFORMANCE.

With Fact 2, we're told that the average number of performances attended PER STUDENT (in the school) is 4, so we can determine that there were (200)(4) = 800 total student-attendences 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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IMHO I can only say that there is certainly an ambiguity in the language of this question.
"Average number of students attending each performance".

There are 2 interpretations:
Interpretation 1: For each performance what was the average number of students attended.
OR
What was the attendance on an average for each performance

Interpretation 2: What was the average of all those students -> who attended each (i.e. all the 8) performances.

With interpretation 1 -> answer choice will be B
With interpretation 2 -> answer choice will be E

My only learning is (although very dicey) is -> not to overcomplicate things and go for interpretation 1. But I am not very sure if will have the time to decide on such things in the actual exam.

Hoping to get response from experts also (especially from e-GMAT experts.


Thanks,
Saurabh (e-GMAT student)

(1) May give several outcomes, such as each student 1 performance, total 200, average 200/8=25, Each student 4, total 800, average=800/8=100; Insufficient.

(2) Number of performance per student is fixed 4, total 200*4=800, average=800/18=100; Sufficient.

The answer is B.
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