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
Weighted averages
This topic has expert replies
-
- Legendary Member
- Posts: 641
- Joined: Tue Feb 14, 2012 3:52 pm
- Thanked: 11 times
- Followed by:8 members
- niketdoshi123
- Master | Next Rank: 500 Posts
- Posts: 210
- Joined: Thu Mar 08, 2012 11:24 pm
- Thanked: 62 times
- Followed by:3 members
If both the schools have same number of classes ,be xgmattesttaker2 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?
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
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
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.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
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.
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
If anyone is interested, we have a free video on weighted averages here: https://www.gmatprepnow.com/module/gmat- ... ics?id=805
Cheers,
Brent
Cheers,
Brent
-
- Legendary Member
- Posts: 641
- Joined: Tue Feb 14, 2012 3:52 pm
- Thanked: 11 times
- Followed by:8 members
Hi Niket,niketdoshi123 wrote:If both the schools have same number of classes ,be xgmattesttaker2 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?
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
Thanks a lot for the excellent explanation. It is clear now.
Best Regards,
Sri
-
- Legendary Member
- Posts: 641
- Joined: Tue Feb 14, 2012 3:52 pm
- Thanked: 11 times
- Followed by:8 members
Hello Brent,Brent@GMATPrepNow wrote: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.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
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
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
-
- Senior | Next Rank: 100 Posts
- Posts: 38
- Joined: Thu Apr 28, 2016 7:17 pm
- Thanked: 1 times
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.
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.
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
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