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M22-09

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Bunuel
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M22-09 [#permalink] New post   16 Sep 2014, 01:16
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What is the average (arithmetic mean) age of all students in the city's schools?


(1) The average (arithmetic mean) age of students in each school in the city is 12 years.

(2) Each school in the city has 70 students.
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Bunuel
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Re M22-09 [#permalink] New post   16 Sep 2014, 01:16
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Official Solution:


What is the average (arithmetic mean) age of all students in the city's schools?

(1) The average (arithmetic mean) age of students in each school in the city is 12 years.

Given that the average age is the same across all schools, the overall average age will also be equal to the average age in each school. Sufficient.

(2) Each school in the city has 70 students.

This statement is clearly insufficient, as it provides no information about the students' ages.


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ncplagge
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Re: M22-09 [#permalink] New post   01 Feb 2018, 16:50
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Hi --

How come we wouldn't need to know how many students were in each of the city's schools and get a weighted average? Is it because the average is the same across all the schools?

Thanks!
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Re: M22-09 [#permalink] New post   01 Feb 2018, 21:11
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ncplagge wrote:
Hi --

How come we wouldn't need to know how many students were in each of the city's schools and get a weighted average? Is it because the average is the same across all the schools?

Thanks!


Yes. If the average is the same for several groups then the overall average would be the average of any of the groups. For example, if the average age of group A is 12 years and the average age of group B is also 12 years, then the overall average age will also be 12 years irrespective of the number of people in the groups. Or using the formula: \(\frac{12N_1 + ... + 12N_k}{N_1 + ... + N_k} = \frac{12(N_1 + ... + N_k)}{N_1 + ... + N_k}=12\) (notice that N1, N2, ..., Nk are the number of students in the schools and all of them are reduced).
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Re: M22-09 [#permalink] New post   06 May 2023, 01:04
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M22-09 [#permalink]
06 May 2023, 01:04
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