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A marketing firm determined that, of 200 households [#permalink]
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29 Dec 2007, 18:40
This topic is locked. If you want to discuss this question please repost it in the respective forum. 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]
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01 Jan 2008, 10:04
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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. Try it on other ones. It will never be confusing again. Attachment:
grouping box.JPG [ 9.17 KiB  Viewed 9171 times ]



CEO
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how is it 15?
200 = 60 + 3B  B + 80
60 = 2b
b=30



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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]
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29 Dec 2007, 19:54
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]
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29 Dec 2007, 20:06
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]
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29 Dec 2007, 20:47
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 1235 times ]



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apparently, we memorized the formula wrong.
http://www.urch.com/forums/318578post2.html



Director
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bmwhype2 wrote:
Could you please post the correct formula because, the link does not open after trying hard!



Director
Joined: 09 Aug 2006
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LM wrote: bmwhype2 wrote: 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



Director
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Re: Set Theory [#permalink]
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01 Jan 2008, 11:44
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.



VP
Joined: 22 Nov 2007
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Re: Set Theory [#permalink]
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03 Jan 2008, 05:57
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



Director
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Re: Set Theory [#permalink]
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03 Jan 2008, 06:20
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]
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04 Feb 2008, 02:05
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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Director
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Re: Set Theory [#permalink]
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04 Feb 2008, 02:44
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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