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24 Nov 2018, 10:00
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C
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Difficulty:
75%
(hard)
Question Stats:
60% (02:36) correct
40%
(02:36)
wrong
based on 281
sessions
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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
24 Nov 2018, 10:08
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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
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
24 Nov 2018, 10:21
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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.
Posted from my mobile device
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.
Posted from my mobile device
