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In a survey conducted for three perfumes, it was found that 40% of the

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In a survey conducted for three perfumes, it was found that 40% of the  [#permalink]

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New post 30 Jan 2019, 03:51
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In a survey conducted for three perfumes, it was found that 40% of the respondents used Fa, 25% used Havoc, 60% used Nido, 16% used none of the three perfumes whereas 15% of the respondents used exactly two of the three perfumes. What % of the respondents used all three perfumes?

A)7%
B)12%
C)13%
D)20%
E)22%
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In a survey conducted for three perfumes, it was found that 40% of the  [#permalink]

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New post 30 Jan 2019, 04:44
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selim wrote:
In a survey conducted for three perfumes, it was found that 40% of the respondents used Fa, 25% used Havoc, 60% used Nido, 16% used none of the three perfumes whereas 15% of the respondents used exactly two of the three perfumes. What % of the respondents used all three perfumes?

A)7%
B)12%
C)13%
D)20%
E)22%


A very straight forward answer..

Total = Sum of each -sum of two together-2*all three+ neither
100=40+25+60-15-2*T+16
2T=25-15+16=26
T=13%

with Venn diagram..
40+25+60 = (a+b+d+e)+(b+c+e+f)+(d+e+f+g)=a+2b+c+2d+3e+2f+g=(a+b+c+d+e+f)+(b+d+f)+2g = (100-16)+15+2g=99+2g
2g=125-99=26...g=13
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Re: In a survey conducted for three perfumes, it was found that 40% of the  [#permalink]

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New post 30 Jan 2019, 04:49
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Total = Use Fa +Use Havoc + Use Nido + Use none - Use 2 of the perfumes - 2*(use all three perfumes) =100%

Translating into numbers:


100= 40+25+60+16-15-2X

where X is the percentage of respondents that used all 3 perfumes.

Solving the previous equation the result is X=13, so C should be the correct answer.
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Re: In a survey conducted for three perfumes, it was found that 40% of the  [#permalink]

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New post 30 Jan 2019, 06:51
selim wrote:
In a survey conducted for three perfumes, it was found that 40% of the respondents used Fa, 25% used Havoc, 60% used Nido, 16% used none of the three perfumes whereas 15% of the respondents used exactly two of the three perfumes. What % of the respondents used all three perfumes?

A)7%
B)12%
C)13%
D)20%
E)22%


let total =100
100=40+25+60+16-15-2(x)
-26=-2x
x=13
IMO C
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Re: In a survey conducted for three perfumes, it was found that 40% of the  [#permalink]

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New post 30 Jan 2019, 18:13
Sir,

I think sum of two together and sum of only two together, both are quite different terms.

chetan2u wrote:
selim wrote:
In a survey conducted for three perfumes, it was found that 40% of the respondents used Fa, 25% used Havoc, 60% used Nido, 16% used none of the three perfumes whereas 15% of the respondents used exactly two of the three perfumes. What % of the respondents used all three perfumes?

A)7%
B)12%
C)13%
D)20%
E)22%


A very straight forward answer..

Total = Sum of each -sum of two together-2*all three+ neither
100=40+25+60-15-2*T+16
2T=25-15+16=26
T=13%

with Venn diagram..
40+25+60 = (a+b+d+e)+(b+c+e+f)+(d+e+f+g)=a+2b+c+2d+3e+2f+g=(a+b+c+d+e+f)+(b+d+f)+2g = (100-16)+15+2g=99+2g
2g=125-99=26...g=13
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Re: In a survey conducted for three perfumes, it was found that 40% of the  [#permalink]

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New post 01 Feb 2019, 18:40
selim wrote:
In a survey conducted for three perfumes, it was found that 40% of the respondents used Fa, 25% used Havoc, 60% used Nido, 16% used none of the three perfumes whereas 15% of the respondents used exactly two of the three perfumes. What % of the respondents used all three perfumes?

A)7%
B)12%
C)13%
D)20%
E)22%



Letting n = the percentage of respondents who used all three perfumes, we can create the equation:

100 = 40 + 25 + 60 - 15 - 2n + 16

100 = 126 - 2n

2n = 26

n = 13

Answer: C
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Re: In a survey conducted for three perfumes, it was found that 40% of the   [#permalink] 01 Feb 2019, 18:40
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