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In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what percentage of those asked favoured more than one of the three proposals?

  1. 10
  2. 12
  3. 17
  4. 22
in Quantitative Aptitude
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Let A=favoured proposal III

B=favoured proposal III

C=favoured proposal III

Here, n(A U B U C)=78

We Knows,

n(AUBUC)= n(A)+n(B)+n(C)-n(A ∩ B)-n(A ∩ C)-n(A ∩ B)+n(A ∩ B ∩ C)

78 = 50 + 30 + 20 - n(A ∩ B) - n(A ∩ C) - n(A ∩ B) + 5.

n(A ∩ B) + n(A ∩ C) + n(A ∩ B) = 27

 

For those who favored exactly 2 proposals we have to subtract n(A ∩ B ∩ C) from n(A ∩ B) , n(A ∩ C) and n(A ∩ B)

n(A ∩ B) + n(A ∩ C) + n(A ∩ B)  - 3*n(A ∩ B ∩ C)

=27-15 =12

 

For those who favored exactly 3 proposals=5

Now, those who favored more than one of the 3 proposals = 12 + 5 =17

 

Hence,Option (C)17 is the correct choice.

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