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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] New post 29 Dec 2007, 17:40
A marketing firm determined that, of 200 households surveyed, 80 use neither Brand A nor 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 households surveyed used both brands of soap.






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Re: Set Theory [#permalink] New post 01 Jan 2008, 09:04
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I use a completely different system for these kinds of questions. It works every single time, as long as there are two groups (if there are three, I use the venn diagram).

Draw a 3 by 3 box, as in the diagram. All rows add down to the bottom row, and all columns add across to the right column. The bottom right box is the total of the whole system.

Fill in what is given, and then infer what is not.

Then answer the question.

In my attached example, the black numbers are given, the red ones are what is inferred.

Once finished, in this question, see that the right column adds all the way down and has one variable:

4x + 140 = 200
x = 15

In this case, the boxes with the question marks are irrelevant, so I leave them alone. In other types of questions, you may fill them in.

Image

Try it on other ones. It will never be confusing again.


[Reveal] Spoiler:
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grouping box.JPG
grouping box.JPG [ 9.17 KiB | Viewed 3559 times ]
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 [#permalink] New post 29 Dec 2007, 18:11
how is it 15?

200 = 60 + 3B - B + 80
60 = 2b
b=30
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 [#permalink] New post 29 Dec 2007, 18:23
I got the same answer, unfortunately my handout doesn't have the solutions, it only gives the answer.
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Re: Set Theory [#permalink] New post 29 Dec 2007, 18:54
inwosu wrote:
A marketing firm determined that, of 200 households surveyed, 80 use neither Brand A nor 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 households surveyed used both brands of soap.


200 total
80 use niether
120 use either A or B or Both
60 use only A
so 60 use B or bothAB

For every AB there are three B
3AB=B
AB+B=60
AB+3AB=60
4AB=60
AB=15

Answer 15
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Re: Set Theory [#permalink] New post 29 Dec 2007, 19:06
Damager wrote:
inwosu wrote:
A marketing firm determined that, of 200 households surveyed, 80 use neither Brand A nor 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 households surveyed used both brands of soap.


200 total
80 use niether
120 use either A or B or Both
60 use only A
so 60 use B or bothAB

For every AB there are three B
3AB=B
AB+B=60
AB+3AB=60
4AB=60
AB=15

Answer 15


thanks for the clarification
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Re: Set Theory [#permalink] New post 29 Dec 2007, 19:47
inwosu wrote:
A marketing firm determined that, of 200 households surveyed, 80 use neither Brand A nor 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 households surveyed used both brands of soap.

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Venn Diagram.PNG [ 15.54 KiB | Viewed 860 times ]

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 [#permalink] New post 29 Dec 2007, 19:48
apparently, we memorized the formula wrong.

http://www.urch.com/forums/318578-post2.html
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 [#permalink] New post 30 Dec 2007, 05:13
bmwhype2 wrote:
apparently, we memorized the formula wrong.

http://www.urch.com/forums/318578-post2.html


Could you please post the correct formula because, the link does not open after trying hard!
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 [#permalink] New post 30 Dec 2007, 12:50
LM wrote:
bmwhype2 wrote:
apparently, we memorized the formula wrong.

http://www.urch.com/forums/318578-post2.html


Could you please post the correct formula because, the link does not open after trying hard!


In the formula A + B + neither - both, A represents all those who use brand A, not just those who use only brand A, and B represents all those who use brand B, not just those who use only brand B. So A = the number who use only brand A (60) plus the number who use both brands (x), and B = the number who use only brand B (3x) plus the number who use both brands (x):

A + B + neither - both
(60 + x) + (3x + x) + 80 - x = 200
140 + 4x = 200
x = 15
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Re: Set Theory [#permalink] New post 01 Jan 2008, 10:44
Ian, I really like this method. I got 30 on this two and like a idiot knew this was going to be wrong. I've seen this type of only A/only B questions in the OG and should have been looking out for it.

Your system seems pretty good! I'm going to start using it. Similar to the Manhattan quad system.

ian7777 wrote:
I use a completely different system for these kinds of questions. It works every single time, as long as there are two groups (if there are three, I use the venn diagram).

Draw a 3 by 3 box, as in the diagram. All rows add down to the bottom row, and all columns add across to the right column. The bottom right box is the total of the whole system.

Fill in what is given, and then infer what is not.

Then answer the question.

In my attached example, the black numbers are given, the red ones are what is inferred.

Once finished, in this question, see that the right column adds all the way down and has one variable:

4x + 140 = 200
x = 15

In this case, the boxes with the question marks are irrelevant, so I leave them alone. In other types of questions, you may fill them in.

Try it on other ones. It will never be confusing again.
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Re: Set Theory [#permalink] New post 03 Jan 2008, 04:57
inwosu wrote:
A marketing firm determined that, of 200 households surveyed, 80 use neither Brand A nor 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 households surveyed used both brands of soap.



N=200
A=60
B=3AB

200=80+60+4AB
AB=15
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Re: Set Theory [#permalink] New post 03 Jan 2008, 05:20
The equation is 200=80+60+x+3x where x is the number of people who used both brands. Therefore x=15.
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Re: Set Theory [#permalink] New post 04 Feb 2008, 01:05
i didnt know there were 3 ways we can do this type of problem

double set matrix
venn
set theory

all in all, i think double set matrix, rather than set theory, is "better" for "two element" problems

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Re: Set Theory [#permalink] New post 04 Feb 2008, 01:44
Draw the venn diagram it would be quick and easy

Out of 200, 80 do not use A,B so the Soap using set is 120

Of 120, 60 people use A

so the remaining 60 includes (soap B+ both the soaps)

but remaining is in the ratio of 1:3(for every one who uses A&B soap, there are 3 users of B)

x+4x=60 => x is 15


Hope this helps.

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Re: Set Theory   [#permalink] 04 Feb 2008, 01:44
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