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VP  D
Joined: 31 Oct 2013
Posts: 1464
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
In a survey conducted for three perfumes, it was found that 40% of the  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 52% (01:59) correct 48% (02:51) wrong based on 31 sessions

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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%
Math Expert V
Joined: 02 Aug 2009
Posts: 7977
In a survey conducted for three perfumes, it was found that 40% of the  [#permalink]

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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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Joined: 30 May 2017
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Re: In a survey conducted for three perfumes, it was found that 40% of the  [#permalink]

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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.
GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 5017
Location: India
Concentration: Sustainability, Marketing
GPA: 4
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Re: In a survey conducted for three perfumes, it was found that 40% of the  [#permalink]

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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%

let total =100
100=40+25+60+16-15-2(x)
-26=-2x
x=13
IMO C
Senior Manager  G
Joined: 09 Aug 2017
Posts: 496
Re: In a survey conducted for three perfumes, it was found that 40% of the  [#permalink]

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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
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8099
Location: United States (CA)
Re: In a survey conducted for three perfumes, it was found that 40% of the  [#permalink]

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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%

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

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