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help me to solve one prob I saw in a test

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by goyalsau » Sun Nov 28, 2010 7:23 am
This is the first time I have seen a problem With Four Overlapping SETS..............

What is the source of the problem.............
Saurabh Goyal
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by rishab1988 » Sun Nov 28, 2010 9:03 am
Dude this problem is crazy.Drawing Venn diagram for this is like showing 4 dimensions on a page.

haha..

Anyway,I doubt you'll ever see such question ever show on GMAT.Maybe when GMAT is scaled upto 60.

I have browsed almost entire internet and I couldn't fnd a solution to that.
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by oddball » Sun Nov 28, 2010 10:25 am
Do you remember the question properly?
I think some data are missing. Only with the informatin you provided it is not possible to solve the problem. :|
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by rishab1988 » Sun Nov 28, 2010 3:07 pm
SOLVED THE QUESTION.

Okay this problem can be solved.I crunched my brain hard and devised a way.This can be done using combinatorics and sets.

Yep you are right combinatorics in sets!

Now ,when there are 2 sets (say A and B).There is just one intersection.You know how to calculate this?

I'll show.

In intersection of elements are two places.

No of ways for choosing first element : 2 [you could either choose A or B]
Now of ways for choosing second element: 1 [after you have chosen ,say A,you are left with just B]

So no of ways = 2*1=2.But wait A intersection B is same as B intersection A,so divide by 2.
No of intersections =1

Similarly in a 3 element set Venn diagram.

No of intersections of 2 elements : (3*2)/2! =3
No of intersections of 3 elements : (3*2*1)3!=1

Now for a 4 element set:

No of intersections of 2 elements : (4*3)/2!=6
No of intersections of 3 elements : (4*3*2)/3!=4
No of intersections of 4 elements : (4*3*2*1)/4!=1

Now,

In a 2 element set

Let A denote only A
B denote only B
and a denote intersection of A and B.
Then total no elements = A+B+a

Similarly in a 3 element set,

Total no of elements : A+B+C+a+b+c+d [ where a,b,and c denote intersection of 2 elements and d denotes intersection of all 3 elements]

Now IN A 4 element set

Total = A+B+C+D+ [a+b+c+d+e+f]+[g+h+i+j]+[k] [ arranged order of intersection]=40

a= A intersection B
b= A and C
c= A and D
d= B and C
e= B and D
f = C and D

g= A and B and C
h= A and B and D
i = A and C and D
j = B and C and D

k= A and B and C and D

Question is what is k?

Now stay here only if you want your brains to be FRIED!

k = 40 - [a+b+c+d+e+f] - [g+h+i+j] - [A+B+C+D]

A+a+b+c+g+h+i+k =37 [English] [Include all those that have A]

B+a+d+e+g+h+j+k = 31 [Spanish]

C+b+d+f+g+i+j+k = 28 [Spanish]

D+b+e+f+h+i+j+k =27 [German]


Adding all of them!!!!!!!

A+B+C+D+2[a+b+c+d+e+f]+3[g+h+i+j]+4k = 123

Substituting:

A+B+C+D+[a+b+c+d+e+f]+[g+h+i+j]+k =40 in the above equation:

[a+b+c+d+e+f]+2[g+h+i+j+k]+3k = 83

WHAT THE HECK!

YOU DIDN'T PROVIDE COMPLETE INFO.

I NEED no students in 2 classes and 3 classes!

I assume no of 2 students = 34
No of 3 students =17

[I WON'T LET MY EFFORT GO WASTE]

34+34+3k=83
3k=15
k=5

or no of students who study all classes = 5

THIS IS NOT A GMAT QUESTION.

THIS IS ATLEAST A 5-10 MINUTE QUESTION
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by Andijansky » Sun Nov 28, 2010 6:46 pm
oddball wrote:Do you remember the question properly?
I think some data are missing. Only with the informatin you provided it is not possible to solve the problem. :|

the thing is I saw it in a test for job application and thought I have to be able to solve being a student who's going to take GMAT,anyway, thank you all!:)
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by goyalsau » Sun Nov 28, 2010 6:49 pm
rishab1988 wrote:Dude this problem is crazy.Drawing Venn diagram for this is like showing 4 dimensions on a page.

haha..
Great Work Rishab, I doubt will i able to do one like this by myself.,

but i must say Your 4 Dimension Thought Could may Give the Great Einstein some sleeping Nightmares,

What to say buddy , I just can't stop Laughing.....................
Saurabh Goyal
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by goyalsau » Sun Nov 28, 2010 6:50 pm
Andijansky wrote: the thing is I saw it in a test for job application and thought I have to be able to solve being a student who's going to take GMAT,anyway, thank you all!:)
Buddy, I have a free suggestion to make, Don't Join that Company , If they ask such question on the Test , Just Wonder what they will do to you when you will join them,,,,,,,,,
Saurabh Goyal
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by Andijansky » Sun Nov 28, 2010 6:52 pm
thnx!:) I'll keep that in mind, and if I get accepted, will convey the message sure:)
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