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A marketing firm determined that, of 200 households surveyed

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A marketing firm determined that, of 200 households surveyed [#permalink] New post 22 Sep 2016, 12:04
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Question Stats:

75% (01:04) correct 25% (09:35) wrong based on 4 sessions
A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used 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
[Reveal] Spoiler: OA

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1 KUDOS received
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Kudos [?]: 1137 [1] , given: 7

Re: A marketing firm determined that, of 200 households surveyed [#permalink] New post 22 Sep 2016, 12:05
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GreenlightTestPrep wrote:
A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used 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


Here's a step-by-step approach using the Double Matrix method.

Here, we have a population of 200 households , and the two characteristics are:
- using or not using Brand A soap
- using or not using Brand B soap

So, we can set up our matrix as follows (where "~" represents "not"):
Image

80 used neither Brand A nor Brand B soap
We can add this to our diagram as follows:
Image

60 used only Brand A soap
We get...
Image

At this point, we can see that the right-hand column adds to 140, which means 140 households do NOT use brand B soap.
Image

Since there are 200 households altogether, we can conclude that 60 households DO use brand B soap.
Image

For every household that used BOTH brands of soap...
Let's let x = # of households that use BOTH brands....
Image

...3 used only Brand B soap.
So, 3x = # of households that use ONLY brand B soap
Image

At this point, when we examine the left-hand column, we can see that x + 3x = 60
Simplify to get 4x = 60
Solve to get x = 15

How many of the 200 households surveyed used BOTH brands of soap?
Since x = # of households that use BOTH brands of soap, the correct answer here is:
[Reveal] Spoiler:
A


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Re: A marketing firm determined that, of 200 households surveyed [#permalink] New post 23 Sep 2017, 16:35
Приветики мальчики и девочки. А как интересно Вы
проводите своё свободное время?
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Re: A marketing firm determined that, of 200 households surveyed [#permalink] New post 24 Sep 2017, 09:01
EvaDanVasG wrote:
Приветики мальчики и девочки. А как интересно Вы
проводите своё свободное время?


The official language of the forum is english. Thus, we would be pleased if you post that way.
However I Google-translated your post and it does not seem to have relevance to this topic.
Re: A marketing firm determined that, of 200 households surveyed   [#permalink] 24 Sep 2017, 09:01
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A marketing firm determined that, of 200 households surveyed

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