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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 we

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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 we

by BTGmoderatorDC » Wed Mar 11, 2020 5:21 pm

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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 attended at least one cultural performance
(2) Last school year, the average number of cultural performance attended per student was 4.



OA B

Source: Official Guide
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Source: — Data Sufficiency |

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Re: Last school year, each of the 200 students at a certain high school attended the school for the entire year. If ther

by Jay@ManhattanReview » Thu Mar 12, 2020 1:18 am

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BTGmoderatorDC wrote: ↑
Wed Mar 11, 2020 5:21 pm
 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 attended at least one cultural performance
(2) Last school year, the average number of cultural performances attended per student was 4.

OA B

Source: Official Guide
To answer the question, we must know which student attended how many programs, this will give us the total attendees.

Let's take each statement one by one.

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

Case 1: Say each of the 200 students attended one program. Thus, the average (arithmetic mean) number of students attending each cultural performance = 200/8 = 25.

Case 2: Say each of the 200 students attended 2 programs. Thus, the average (arithmetic mean) number of students attending each cultural performance = 200*2/8 = 50.

No unique answer. Insufficient.

(2) Last school year, the average number of cultural performances attended per student was 4.

=> Total no. of attendees = 200*4 = 800

Thus, the average (arithmetic mean) number of students attending each cultural performance = 800/8 = 100. Sufficient

The correct answer: B

Hope this helps!

-Jay
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