## The average number of students per class at School X is 25 and the average number of students per class at School Y is

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### The average number of students per class at School X is 25 and the average number of students per class at School Y is

by BTGmoderatorDC » Thu Nov 25, 2021 12:08 am

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## Global Stats

The average number of students per class at School X is 25 and the average number of students per class at School Y is 33. Is the average number of students per class for both schools combined less than 29?

1) There are 12 classes in school X.
2) There are more classes in school X than in school Y.

OA B

Source: Manhattan Prep

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### Re: The average number of students per class at School X is 25 and the average number of students per class at School Y

by [email protected] » Thu Nov 25, 2021 6:46 am

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## Global Stats

BTGmoderatorDC wrote:
Thu Nov 25, 2021 12:08 am
The average number of students per class at School X is 25 and the average number of students per class at School Y is 33. Is the average number of students per class for both schools combined less than 29?

1) There are 12 classes in school X.
2) There are more classes in school X than in school Y.

OA B

Source: Manhattan Prep
Important principle. When combining the averages (means) of two groups, the group with the most members will have the greater effect on the combined averages. That is, the combined average will be closer to the group with the most members.

Example:
Group A has an average age of 10 years
Group B has an average age of 20 years

- If the two groups have the same number of members, the combined average will be 15 (right in the middle).
- If group A has more members than group B, the combined average will be less than 15 (closer to group A's average of 10).
- If group B has more members than group A, the combined average will be more than 15 (closer to group B's average of 20).

Statement 1: no information about the number of classes at school Y
INSUFFICIENT

Statement 2: If school X has more classes, the combined average will be closer to 25 than to 33
Since 29 is halfway between 25 and 33, we know that the combined average number of students per class for both schools MUST BE less than 29
SUFFICIENT