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Music High School - Venn or Double Matrix

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Music High School - Venn or Double Matrix

by mmslf75 » Fri Jan 01, 2010 4:20 am
All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 119 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only?

A) 30
B) 51
C) 60
D) 85
E) 119



OA is B

Guys, question here, how should we do this with DOUBLE MATRIX?


Source MGMAT Test 4
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by truplayer256 » Fri Jan 01, 2010 8:58 am
Instead of using a double-matrix for this problem, let's use our common sense.

Let's assume that there are x students in Music High School that are either in the band, the orchestra, or both.

If 80 percent of the students are in only one group, then this means that 20 percent are in both.

.80(x)= only one group

.20(x)= both

The 119 students in the band includes both students that are in the band as well as in the band and orchestra, so:

119-.20(x)=# of students who are only in the band.

The problem tells us that 50 percent of the students are in the band only, so let's substitute this value into the expression.


119-.20(x)=.50(x)

x=170

We know that x-.50(x)-.20(x)=.30(x) of the students are in the orchestra only, so the answer to the problem would be .30(170)=51.
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by poonammarwah » Fri Jan 01, 2010 10:57 pm
Hi,
I am also curious to know, can this question be solved by double matrix?

Please help.

P.S: Please do not suggest other method as I know how to solve it without double matrix.
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by thephoenix » Sat Jan 02, 2010 2:08 am
double matrix system attached

but its advicable to solve this one with venn diag
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by poonammarwah » Mon Jan 04, 2010 3:21 pm
Thank You! thephoenix
As per MGMAT we should do this type of Q(2 team) with double matrix and otheres(3 variables/team) with Venn. This Q is simple if we do it without double matrix. Could you please help me, how to identify this type of Q so that I do not try to solve them through double matrix.

Also pl let me know the Venn Diag method for this q and why it is advisable to solve it though venn diag.

Thanks
Poonam
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by thephoenix » Tue Jan 05, 2010 3:00 am
poonammarwah wrote:Thank You! thephoenix
As per MGMAT we should do this type of Q(2 team) with double matrix and otheres(3 variables/team) with Venn. This Q is simple if we do it without double matrix. Could you please help me, how to identify this type of Q so that I do not try to solve them through double matrix.

Also pl let me know the Venn Diag method for this q and why it is advisable to solve it though venn diag.

Thanks
Poonam
venn dia soln attached

Double matrix is indeed a quicker method but if clues are complicated then its always easier to adapt venn dig method as it gives a pictorial view and one can easily use the clues

HTH
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by poonammarwah » Tue Jan 05, 2010 7:30 pm
Thanks!
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by odod » Wed Jan 06, 2010 8:29 am
Can someone explain this part of the above answer . It was the answer above from the venn diagram

and y+z=.5n volet + blue

y+z=.5n zy=.2n

from 2 .5n+.2n=119 n=170z=.3 * 170=51


The boxes are supposed to be arrows.

Thanks
ODOD
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by thephoenix » Sun Jan 17, 2010 7:34 am
odod wrote:Can someone explain this part of the above answer . It was the answer above from the venn diagram

and y+z=.5n volet + blue

y+z=.5n zy=.2n

from 2 .5n+.2n=119 n=170z=.3 * 170=51


The boxes are supposed to be arrows.

Thanks
tot is n
50 % of n i.e 0.5n is in band only which is yellow portion -------> x=0.5 n
logically rest 50% is y+z ( the violet and blue portion)---->y+z=0.5 n

now x+z=0.8n , therefore z=0.8n-x=0.3n ; hence y=0.5n-z=0.2n
hence x=0.5n; y=0.2n and z=0.3n

x+y=0.7n----->0.7n=119--->n=170----> z=0.3*170=51
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