In a poll, 1200 participants expressed their preferences among

Question

In a poll, 1200 participants expressed their preferences among candidates A, B, and C. Candidate A was favored by 54% of respondents, candidate B by 48%, and candidate C by 42%. If 30% of the respondents favored both candidates A and B, what is the maximum possible number of respondents who favored only candidate C?

(A) 25% 
(B) 28% 
(C) 30% 
(D) 38% 
(E) 40%

There are 1200 respondents to a poll, each favouring their preference for candidates A, B, and C. 54% favoured A, 48% favoured B, and 42% favoured C, and 30% favoured both A and B. What is the largest possible number of respondents favouring C, but not C&B, nor C&A?

Archit3110 · Answer

group over lap
total 1200
A 648 , B 576 and C 504
1200 = 648+576+504 - ( 360+x)
x is only C
x = 168
max can be of only C 504- 168 ; 336 /1200 ;
28%

nikorohr · Answer

maybe this image makes it clearer

ischerry · Answer

I didn't bother with the number 1200. 
In order for Only C to be as big as possible, I considered that there were no respondents who favored all three.

Only C = C - ( B&C + A&C )
Only C = 42% - ( B&C + A&C )
 B&C + A&C  =  x 
Only C = 42% -  x

100% = (A+B+C) - (A&B +  B&C + A&C )
100% = (A+B+C) - (A&B +  x )
100% = (54% + 48% + 42%) - 30% -  x 
100% = 114% -  x 
 x  = 14%

Only C = 42% - 14% = 28%

I'd like someone to verify for me that the method is correct

kevincan · Answer

What percent favored either A or B?

ineedbananas · Answer

how do you make the assumption that there is no respondents who favor all three?

gchandana · Answer

Hi  ineedbananas ,

I don't think that assumption is valid here.

If you see, it is given that 30% favoured both A and B (this could include C as well, as it is not mentioned as  A and B but not C ), then A alone would be 24% (54 - 30), B alone would be 18% (48 - 30), and if we sum it up (30 + 24 + 18), we get 72%.

Now C can have at most 28%.

Hope this helps!

siddharth_ · Answer

Bunuel  can you kindly review this approach?

1200 is not req.

We want to maximise only C.
In the 3 circles venn diagram for A,B,C - lets keep C completely separate.
Now, A union B = 72%. (A + B - A&B = 102% - 30% = 72%)

So the value of only_C cannot be greater than 28%.

In a poll, 1200 participants expressed their preferences among

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