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In a survey of political preferences, 85% of those asked were in favou

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In a survey of political preferences, 85% of those asked were in favou  [#permalink]

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New post 24 Nov 2018, 09:00
1
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A
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Difficulty:

  65% (hard)

Question Stats:

53% (02:40) correct 47% (02:52) wrong based on 30 sessions

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GMATbuster's Weekly Quant Quiz#10 Ques #1


For Questions from earlier quizzes: Click Here


In a survey of political preferences, 85% of those asked were in favour of at least one of the three candidates – Ann, Bann and Cann. 52% of those asked favoured Ann, 35% favoured Bann and 25% favoured Cann. If 10% favoured all the three candidates, what percentage of those asked favoured more than one of the three candidates?
A) 7
B) 10
C) 17
D) 27
E) 37

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Re: In a survey of political preferences, 85% of those asked were in favou  [#permalink]

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New post 24 Nov 2018, 09:08
1
For 3 overlapping sets:
Total = A + B + C - (sum of choices where 2 sets are preferred out of three) - 2*(all three preferred) + None preferred
100 = 52 + 35 + 25 - x - 2*10 + 15
100 = 107 - x
x = 7

Question asks for how many of those asked preferred more than one. This is equal to how many preffered 2 or all three = 7 + 10 = 17

Hence Option C
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Re: In a survey of political preferences, 85% of those asked were in favou  [#permalink]

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New post 24 Nov 2018, 09:21
1
Lets say total Number of people were 100. Out of that 85 of them supported atleast one.
So rest 15 supported no one.

We can directly use the formula

A + B + C = (A) + (B) +(C) -(A+B) - (A+C) - (B+C) + (A+B+C)

85 = 52+35+25-(A+B)-(A+C)-(B+C) +10
(A+B) +(A+C)+(C+B) = 37

Now in 37 people supporting all three are counted thrice

So 37-20

= 17 Ans.

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Re: In a survey of political preferences, 85% of those asked were in favou  [#permalink]

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New post 24 Nov 2018, 09:22
85%= A+B+C-AnB-BnC-CnA-2(AnBnC)
85= 52+35+25-AnB-BnC-CnA-20
AnB+BnC+CnA= 92-85= 7
Thus number of candidates who supported more than one
= 7+10= 17%

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Re: In a survey of political preferences, 85% of those asked were in favou  [#permalink]

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New post 24 Nov 2018, 09:56
gmatbusters wrote:

GMATbuster's Weekly Quant Quiz#10 Ques #1


For Questions from earlier quizzes: Click Here


In a survey of political preferences, 85% of those asked were in favour of at least one of the three candidates – Ann, Bann and Cann. 52% of those asked favoured Ann, 35% favoured Bann and 25% favoured Cann. If 10% favoured all the three candidates, what percentage of those asked favoured more than one of the three candidates?
A) 7
B) 10
C) 17
D) 27
E) 37




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Re: In a survey of political preferences, 85% of those asked were in favou  [#permalink]

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New post 24 Nov 2018, 10:02
[quote="ankitahyd2013"][quote="gmatbusters"]

GMATbuster's Weekly Quant Quiz#10 Ques #1


For Questions from earlier quizzes: Click Here


In a survey of political preferences, 85% of those asked were in favour of at least one of the three candidates – Ann, Bann and Cann. 52% of those asked favoured Ann, 35% favoured Bann and 25% favoured Cann. If 10% favoured all the three candidates, what percentage of those asked favoured more than one of the three candidates?
A) 7
B) 10
C) 17
D) 27
E) 37


% of people favouring Ann =52%
% of people favouring Bann=35%
% of people favouring Cann=25%
% of people favouring all three=10%
% of people favouring more than one canditate=[(52-10)+(35-10)+(25-10)-85]
=7%



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Re: In a survey of political preferences, 85% of those asked were in favou  [#permalink]

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New post 24 Nov 2018, 14:16
This question can be answered in 2 ways,

1) Total = In favor of A + In favor of B + In favor of C + In favor of neither - In favor of two + In favor of all three
that is, 100 = 52+35+25+15- In favor of two + 10
that is, In favor of two = 37
In favor of two includes In favor of all three twice as well, so we need to subtract that out.
Hence, required answer = 37 - 2*10 = 17 = C.

2) Total = In favor of A + In favor of B + In favor of C + In favor of neither - In favor of two only - 2*In favor of all three
that is, 100 = 52+35+25+15- In favor of two only - 2*10
that is, In favor of two only = 7
In favor of 2 only does not include In favor of all three, so we need to add it.
Hence, required answer = 7 + 10 = 17 = C.
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Re: In a survey of political preferences, 85% of those asked were in favou &nbs [#permalink] 24 Nov 2018, 14:16
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