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Super brutal PS question - Sets

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by rishab1988 » Mon Nov 29, 2010 1:00 am
The total number of regions possible in a set includes all regions,for example,in a two element set [ A and B] the total number of regions is 4-The region called only A,only B,A and B,and neither A nor B.Let a denote the total number regions possible in a 4 element set,b denote the total number of regions in a 6 element set,and c denote the sum of a and b,then which of the following is the LEAST greater integer than c?

a) 33
b) 45
c) 74
d) 84
e) 91

Do this now!

The second question derived from the first one

Which of the following prime numbers is the LEAST that evenly divides c?

a) 5
b) 11
c) 17
d) 29
e) 37

I'm just posting questions that I have designed myself.These are not my doubts..
Last edited by rishab1988 on Mon Nov 29, 2010 1:32 am, edited 3 times in total.
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by shovan85 » Mon Nov 29, 2010 1:24 am
rishab1988 wrote:The total number of regions possible in a set includes all regions,for example,in a two element set [ A and B] the total number of regions is 4-The region called only A,only B,A and B,and neither A nor B.Let a denote the total number regions possible in a 4 element set,b denote the total number of regions in a 6 element set,and c denote the sum of a and b,then which of the following is the LEAST greater integer than c?

a) 33
b) 45
c) 66
d) 100
e) 146
Is it D?

Total number of regions possible in a set includes all regions in a two element set = 4 (2^2)
Total number of regions possible in a set includes all regions in a 3 element set = 8 (2^3)

These two I drew Venn diagram and checked.

Thus, I think there could be a general formula where all the sets intersecting each produce 2^n regions. (n is number of elements)

So, for 4 elements = 2^4 = 16
for 6 elements = 2^6 = 64

Thus c = 16+64 = 80.

Least greater integer to 80 is 100.
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by kvcpk » Mon Nov 29, 2010 1:25 am
Number of regions in an n-element set = 2^n
Hence number of regions in 4 element set = 2^4 = 16
number of regions in 6 element set = 2^6 = 64

c= a+b = 80

hence least greatest integer than c = 100

IMO D.

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by rishab1988 » Mon Nov 29, 2010 1:29 am
the OA was D

Try doing the last question.
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