There is a survey conducted on sports personalities among 1000 people. They are asked to name their favourite sportsperson. The survey names 6 people, namely A,B,C,D,E&F. Out of this survey, 7 people do not like any of the 6 personalities. 953 people like A, 920 like B, 930 like C, 900 like D, 875 like E and 880 like F. Given the scenario, what is the minimum no of people who like all the 6?
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vipulgoyal
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7 do not like anybody out of 1000
i.e. people who like at least 1 of the 6 are 993
For maximum overlap
Smallest must be part of all sets i.e. 875
lets say these people are named from 1 to 993
people who like
A - 1 to 953
B - 1 to 920
C - 1 to 930
D - 1 to 900
E - 1 to 875
F - 1 to 880
Hence 1 to 875 like all 6
i.e. 875 people(maximum)
For Minimum overlap
we can identify this easily by taking the smallest 2 sets
and trying to figure out what could be the minimum overlap between them
E and F in this case are smallest sets
lets just re-position F in the above table
people who like
A - 1 to 953
B - 1 to 920
C - 1 to 930
D - 1 to 900
E - 1 to 875
F - 114 to 993 = 880 people
so 114 to 875 like all 6
i.e. 762 people(minimum)
i.e. people who like at least 1 of the 6 are 993
For maximum overlap
Smallest must be part of all sets i.e. 875
lets say these people are named from 1 to 993
people who like
A - 1 to 953
B - 1 to 920
C - 1 to 930
D - 1 to 900
E - 1 to 875
F - 1 to 880
Hence 1 to 875 like all 6
i.e. 875 people(maximum)
For Minimum overlap
we can identify this easily by taking the smallest 2 sets
and trying to figure out what could be the minimum overlap between them
E and F in this case are smallest sets
lets just re-position F in the above table
people who like
A - 1 to 953
B - 1 to 920
C - 1 to 930
D - 1 to 900
E - 1 to 875
F - 114 to 993 = 880 people
so 114 to 875 like all 6
i.e. 762 people(minimum)
Thanks guys for the replies...
I had worked out this question on some test site and got it wrong.. Here goes the answer explanation given by them... So if you guys get a clue please pour in your views, because logically it did not make any sense to me.
First - No of ppl who like at least one - 993
Ppl who like
A-953 B-920 C-930 D-900 E- 875 F-880
Now find the no of people who do not like the above by subtracting above from 993. Thus the no of people who do not like
A -40 B- 73 C -63 D- 93 E - 118 F - 113
Summing up all the above we get - 500
Now for the minimum value, take the difference between 993 and 500. This is nothing but the no of people who don't like exactly one. Thus the minimum no of people who like all 6 is 443.
Numbers have of course been changed!. So please help me out if you understand the underlying principle!
I had worked out this question on some test site and got it wrong.. Here goes the answer explanation given by them... So if you guys get a clue please pour in your views, because logically it did not make any sense to me.
First - No of ppl who like at least one - 993
Ppl who like
A-953 B-920 C-930 D-900 E- 875 F-880
Now find the no of people who do not like the above by subtracting above from 993. Thus the no of people who do not like
A -40 B- 73 C -63 D- 93 E - 118 F - 113
Summing up all the above we get - 500
Now for the minimum value, take the difference between 993 and 500. This is nothing but the no of people who don't like exactly one. Thus the minimum no of people who like all 6 is 443.
Numbers have of course been changed!. So please help me out if you understand the underlying principle!
