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Weighted averages

by gmattesttaker2 » Sat Aug 11, 2012 11:32 pm
Hello,

Can you please help with this problem? I was not clear with the explanation given in the book.

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

Thanks a lot for your help.

Best Regards,
Sri
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by niketdoshi123 » Sun Aug 12, 2012 12:06 am
gmattesttaker2 wrote:Hello,

Can you please help with this problem? I was not clear with the explanation given in the book.

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?
If both the schools have same number of classes ,be x
then average # of students per class for both schools combined = 25*x + 33*x/2x = 58x/2x = 29
So , if the # of classes in school Y were more than that in school Y, then the average students per class for both class combined would have been less than 29.

Statement 1:
# of classes in school X = 12
We don't know about the # of classes in school Y.
Hence insufficient

Statement 2:
# of classes in school X > # of classes in school Y
This confirms our finding and therefore we can conclude that the average students per class for both class combined is less than 29.

Hence sufficient

The correct answer is B
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Weighted averages

by Brent@GMATPrepNow » Sun Aug 12, 2012 6:59 am
gmattesttaker2 wrote: 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
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

Answer = B

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Tue Aug 28, 2018 1:51 pm, edited 1 time in total.
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by Brent@GMATPrepNow » Sun Aug 12, 2012 7:01 am
If anyone is interested, we have a free video on weighted averages here: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

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by gmattesttaker2 » Sun Aug 12, 2012 8:22 pm
niketdoshi123 wrote:
gmattesttaker2 wrote:Hello,

Can you please help with this problem? I was not clear with the explanation given in the book.

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?
If both the schools have same number of classes ,be x
then average # of students per class for both schools combined = 25*x + 33*x/2x = 58x/2x = 29
So , if the # of classes in school Y were more than that in school Y, then the average students per class for both class combined would have been less than 29.

Statement 1:
# of classes in school X = 12
We don't know about the # of classes in school Y.
Hence insufficient

Statement 2:
# of classes in school X > # of classes in school Y
This confirms our finding and therefore we can conclude that the average students per class for both class combined is less than 29.

Hence sufficient

The correct answer is B
Hi Niket,

Thanks a lot for the excellent explanation. It is clear now.

Best Regards,
Sri
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by gmattesttaker2 » Sun Aug 12, 2012 9:07 pm
Brent@GMATPrepNow wrote:
gmattesttaker2 wrote: 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
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

Answer = B

Cheers,
Brent
Hello Brent,

Hope all is well. Thank you very much for the excellent explanation. It is clear now. Also, thanks for sharing the tutorial link. It is one of the finest explanations that I have ever come across for weighted averages.

Best Regards,
Sri
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by Gurpreet singh » Mon Jun 20, 2016 11:24 pm
You could also plugin values

Statement one is not sufficient as we are not aware of no of classes in school Y
statement 2. More classes in x then in y.
Let x=12 and y=11

Total classes= 23.(x+y)

weighted avg=12/23*29+11/23*29=663/23=28.82<29 Hence statement 2 is sufficient.
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by [email protected] » Tue Jun 21, 2016 10:08 am
Hi All,

In this DS question, we're given some specific information to start off with. We're told that:
1) The average number of students per class at School X is 25
2) The average number of students per class at School Y is 33

We're asked if the average for ALL classes at both Schools is LESS than 29. This is a YES/NO question. Before we deal with the two Facts, we can 'rewrite' this prompt...

IF there were equal numbers of classes at each School, then the average number of students per class for BOTH Schools would be (25+33)/2 = 29. If there are MORE classes at School X than at School Y, then the average DECREASES; if there are MORE classes at School Y than at School X, then the average INCREASES. So when the question asks if the average for both Schools is LESS than 29, it's really asking if there are MORE classes at School X than at School Y...

1) There are 12 classes in School X.

This Fact tells us NOTHING about the number of classes at School Y.
Fact 1 is INSUFFICIENT.

2) There are more classes in School X than in School Y.

This Fact provides information that PROVES that the average MUST be less than 29. The answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich
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