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

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Question Stats:

62% (01:30) correct
37% (04:14) wrong based on 8 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?

Re: A marketing firm determined that, of 200 households surveyed [#permalink]
22 Sep 2016, 12:05

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Expert's post

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"):

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

60 used only Brand A soap We get...

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

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

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

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

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:

Re: A marketing firm determined that, of 200 households surveyed [#permalink]
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.

greprepclubot

Re: A marketing firm determined that, of 200 households surveyed
[#permalink]
24 Sep 2017, 09:01