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# A marketing firm determined that, of 200 households

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A marketing firm determined that, of 200 households [#permalink]

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28 Apr 2008, 18:14
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A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 usd only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?
A. 15
B. 20
C. 30
D. 40
E. 45

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28 Apr 2008, 18:55
Total Household = 200
Number of household who do not use any brands of soap = 80

Number of household who use any brands of soap = 200 - 80 = 120
Number of household who use brands A of soap = 60

Say x people used both brands, then 3*x = 3x people used only brand B.

As per Set theory
120 = 60 + 3x - x
=> 2x = 60
=> x = 30

Director
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28 Apr 2008, 19:30
Sorry got wrong calculation. Questions said "every household that used both brands of soap, 3 used only Brand B soap."

So if Say x people used both brands, then 3*x = 3x people used only brand B.
Then total number of people using brand B = 3x + x = 4x

So As per Set theory
120 = 60 + 4x - x
=> x = 20

Director
Joined: 20 Feb 2008
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Schools: Kellogg Class of 2011
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28 Apr 2008, 20:59
See attached
Attachments

untitled1.JPG [ 16.55 KiB | Viewed 1038 times ]

SVP
Joined: 04 May 2006
Posts: 1902
Schools: CBS, Kellogg
Followers: 23

Kudos [?]: 1121 [0], given: 1

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28 Apr 2008, 21:12
abhijit_sen wrote:

Abhijit, thank for your support, but still be wrong!

jbpayne wrote:
See attached

thank jbpayne, but I am not a fan of diagram, it make me confused!

I like the equation:
Total = group A + group B - group (AB)...
and I am trying to set it up!
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Director
Joined: 20 Feb 2008
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Location: Texas
Schools: Kellogg Class of 2011
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28 Apr 2008, 21:53
The equation also works, but you need to know how to use the diagram as well. Try using the equation when you have three different groups instead of just two. It won't work nearly as easily as a picture.
Manager
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29 Apr 2008, 04:26
abhijit_sen wrote:
Sorry got wrong calculation. Questions said "every household that used both brands of soap, 3 used only Brand B soap."

So if Say x people used both brands, then 3*x = 3x people used only brand B.
Then total number of people using brand B = 3x + x = 4x

So As per Set theory
120 = 60 + 4x - x
=> x = 20

Hey Abhijit,
Brother u are close but u made a silly mistake
3x people used only brand B.
so it is
120=60(only A)+3x(Only B)+x(Both)
Ans is 15
Director
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29 Apr 2008, 14:24
Just a bad day. Getting couple of wrongs do not know why? May be over worked.
Formula still holds correctly. Rohit pointed out well. Cheers mate.
Re: Set problem   [#permalink] 29 Apr 2008, 14:24
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