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# 3 classes X,Y,Z take tests.The average score of X is 83,the

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Intern
Joined: 04 Nov 2007
Posts: 45
3 classes X,Y,Z take tests.The average score of X is 83,the  [#permalink]

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09 Mar 2008, 10:53
3 classes X,Y,Z take tests.The average score of X is 83,the average score of Y is 76,average score of Z is 85.The average score of X and Y is 79,the average score of Y and Z is 81.What is the average score of all 3 classes?

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Intern
Joined: 25 Feb 2008
Posts: 14
Re: Average of all 3 classes  [#permalink]

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09 Mar 2008, 16:05
Did you miss including the average of X and Z in the question ?
SVP
Joined: 29 Aug 2007
Posts: 2410
Re: Average of all 3 classes  [#permalink]

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10 Mar 2008, 00:19
Vemuri wrote:
3 classes X,Y,Z take tests.The average score of X is 83,the average score of Y is 76,average score of Z is 85.The average score of X and Y is 79,the average score of Y and Z is 81.What is the average score of all 3 classes?

x/n = 83
x = 83n

y/m = 76
y = 76m

z/k = 85
z = 85k

(x+y)/(n+m) = 79
(83n + 76m) / (n+m) = 79
83n + 76m = 79n + 79m
4n = 3m

(y + z) / (m+k) = 81
76m + 85k = 81m + 81k
4k = 5m
4n = 3m
n= 3m/4

4k = 5m
k = 5m/4

(x + y + z) / (m+n+k) = ?
= (83n + 76m + 85k) / (n+m+k)
= 83 (3m/4) + 76m + 85(5m/4) / (3m/4 + m + 5m/4)
= [{83 (3m) + 76m (4) + 85(5m) } / 4] / (12m/4)
= (249m + 304m + 425m) / 12m
= 978m/12m
= 81.5
hope i did not do any miscalculation. if any, will correct.
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Intern
Joined: 04 Nov 2007
Posts: 45
Re: Average of all 3 classes  [#permalink]

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10 Mar 2008, 10:31
Wow !!! Way to go. 81.5 is the right answer. Is this the only way to solve this problem?
VP
Joined: 28 Dec 2005
Posts: 1472
Re: Average of all 3 classes  [#permalink]

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10 Mar 2008, 12:31
i took same approach above, i couldnt see any other way to do it. little time consuming, and many places where you can mess up your math.

i dont know if i could do it in 2 minutes
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1252
Re: Average of all 3 classes  [#permalink]

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10 Mar 2008, 15:40
2
Did you know that one can deduce the ratio of the number of students in each class from the distances between the class averages and the overall average?

If a<b<c are the average of group A, the average of A U B, and the average of B respectively,

|A|/|B| = (c -b)/(b -a)

You can use this as long as A and B are mutually exclusive

Let x,y,z be the number in each of X, Y, Z

x/y = (79 - 76)/(83 - 79) = 3/4

y/z =(85 - 81)/(81 - 76)= 4/5

x:y:z= 3:4:5, so x=3k, y=4k, z= 5k, where k is an integer. For simpilicity, assume k=1

So the overall average is (83(3) + 76(4) + 85(5))/12 =(12(80) + 9 - 16 + 25)/12 = 80 + 18/12 = 81.5
Manager
Joined: 12 Feb 2008
Posts: 175
Re: Average of all 3 classes  [#permalink]

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10 Mar 2008, 16:09
great explanations here!
Intern
Joined: 04 Nov 2007
Posts: 45
Re: Average of all 3 classes  [#permalink]

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10 Mar 2008, 19:39
1
kevincan wrote:
Did you know that one can deduce the ratio of the number of students in each class from the distances between the class averages and the overall average?

If a<b<c are the average of group A, the average of A U B, and the average of B respectively,

|A|/|B| = (c -b)/(b -a)

You can use this as long as A and B are mutually exclusive

Let x,y,z be the number in each of X, Y, Z

x/y = (79 - 76)/(83 - 79) = 3/4

y/z =(85 - 81)/(81 - 76)= 4/5

x:y:z= 3:4:5, so x=3k, y=4k, z= 5k, where k is an integer. For simpilicity, assume k=1

So the overall average is (83(3) + 76(4) + 85(5))/12 =(12(80) + 9 - 16 + 25)/12 = 80 + 18/12 = 81.5

This sounds like a shorter method. But, I am not sure I understood it. Can you please elaborate the concept?

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Re: 3 classes X,Y,Z take tests.The average score of X is 83,the  [#permalink]

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23 Mar 2018, 05:49
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Re: 3 classes X,Y,Z take tests.The average score of X is 83,the &nbs [#permalink] 23 Mar 2018, 05:49
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