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Last school year, each of the 200 students at a certain high school at

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Last school year, each of the 200 students at a certain high school at [#permalink]

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New post 26 Jun 2017, 02:56
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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.

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Re: Last school year, each of the 200 students at a certain high school at [#permalink]

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New post 26 Jun 2017, 04:09
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Bunuel 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.


(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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Re: Last school year, each of the 200 students at a certain high school at [#permalink]

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New post 26 Jun 2017, 05:33
Bunuel 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.


(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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Re: Last school year, each of the 200 students at a certain high school at [#permalink]

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New post 26 Jun 2017, 07:32
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Bunuel 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.


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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Re: Last school year, each of the 200 students at a certain high school at [#permalink]

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New post 03 Jul 2017, 01:58
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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
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Re: Last school year, each of the 200 students at a certain high school at [#permalink]

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New post 17 Nov 2017, 12:31
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2
Bunuel 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
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Re: Last school year, each of the 200 students at a certain high school at [#permalink]

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New post 21 Nov 2017, 01:35
broall wrote:
Bunuel 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.


(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.


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.
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Re: Last school year, each of the 200 students at a certain high school at [#permalink]

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New post 25 Nov 2017, 23:51
1
Soteria wrote:
broall wrote:
Bunuel 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.


(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.


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.
Re: Last school year, each of the 200 students at a certain high school at   [#permalink] 25 Nov 2017, 23:51
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