Mean Problem

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sampath: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Thu May 19, 2011 9:20 pm

by sampath » Wed Jul 06, 2011 12:55 am

What is the mean age of all students of the city's schools?
1. The average age of the students in each of the city's schools is 12
2. The number of students in each of the city's schools is 70

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Source: Beat The GMAT — Data Sufficiency | Wed Jul 06, 2011 12:55 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Jul 06, 2011 1:18 am

sampath wrote:What is the mean age of all students of the city's schools?
1. The average age of the students in each of the city's schools is 12
2. The number of students in each of the city's schools is 70

Statement 1: Say, there are n schools in the city with N1, N2, ..., Nn students in them.
Therefore, total age of the students of all the schools = (12*N1 + 12*N2 + ... + 12*Nn) = 12*(N1 + N2 + ... + Nn)
Therefore, average age of all students of the city's schools = (Total age of all the students of the city's schools)/(Total number of students of the city's schools) = (12*(N1 + N2 + ... + Nn))/(N1 + N2 + ... + Nn) = 12

Sufficient.

Statement 2: We don't know the number of schools in the city or the total or average age of the students in each school.

Not sufficient

The correct answer is A.

Last edited by Anurag@Gurome on Wed Jul 06, 2011 2:39 am, edited 1 time in total.

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sampath: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Thu May 19, 2011 9:20 pm

by sampath » Wed Jul 06, 2011 1:48 am

Thanks for the reply Anurag. But I have a question (perhaps a mental block that I can't seem to get around..) but if in the first stem, I assume that there N1, N2...Nn (n - some finite number) of schools and as each school's average equals 12, 12=S1/N1 ===>S1=12(N1), S2= 12(N2) and so on..
So shouldn't the average of all the (N1...Nn)schools equal =>

(S1+S2+S3...Sn)/(N1+N2+Nn)===>(12(N1)+12(N2)...+12(Nn)/(N1+N2...Nn)=12

Thus giving answer as A. Please help. Thanks.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Jul 06, 2011 2:37 am

Thanks for pointing that out sampath.
You're correct. I'm editing my reply.

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amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Fri Jul 08, 2011 2:28 am

clean a here as sum will be multiple of 12.

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