Super brutal PS question - Sets

[rishab1988]

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..

[shovan85]

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.

[kvcpk]

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.

What is OA?

[rishab1988]

the OA was D

Try doing the last question.