Music High School - Venn or Double Matrix

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.

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.

double matrix system attached

but its advicable to solve this one with venn diag

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

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

Thanks!

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 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