Mean Problem

[sampath]

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

[Anurag@Gurome]

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.

[sampath]

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.

[Anurag@Gurome]

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

[amit2k9]

clean a here as sum will be multiple of 12.