BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Super brutal PS question - Sets

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 332
Joined: Tue Feb 09, 2010 3:50 pm
Thanked: 41 times
Followed by:7 members
GMAT Score:720

Super brutal PS question - Sets

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.
Top
Source: — Problem Solving |
User avatar
Community Manager
Posts: 991
Joined: Thu Sep 23, 2010 6:19 am
Location: Bangalore, India
Thanked: 146 times
Followed by:24 members

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.
If the problem is Easy Respect it, if the problem is tough Attack it
Top
User avatar
Legendary Member
Posts: 1893
Joined: Sun May 30, 2010 11:48 pm
Thanked: 215 times
Followed by:7 members

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.

What is OA?
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 332
Joined: Tue Feb 09, 2010 3:50 pm
Thanked: 41 times
Followed by:7 members
GMAT Score:720

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

Try doing the last question.
Top
Post new topic Post Reply
• Page 1 of 1