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I was reading one of walker's posts today and something [#permalink]

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18 Jul 2008, 13:42

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I was reading one of walker's posts today and something about it clicked with how I see Venn Diagrams and Set Theory. It's nothing too crazy, it's just that I'm not one to jump right to a formula...I like the visual part of the Venn diagrams and so I use them, but they're not always the easiest (or quickest) way to solve a problem.

If you have 3 overlapping groups, lets says athletes in school. Soccer players, basketball players, and golfers.

total of 100 athletes, some play all three, some play only 2, but everyone plays at least 1 sport.

Lets say you have 60 basketabll players, 33 soccer players, and 14 golfers. The formula to set this up would be:

100 = (S + B + G) - SB - SG - BG - SBG

Lets substitute in what we know:

100 = 33 + 60 + 14 - SB - SG - BG - SGB

Of course, we don't yet have enough information to answer the question, but this seems like a much better way to organize the problem rather than in picture/diagram form.

Lets say we also know "Everyone that plays Golf also plays basketball."

100 = 30 + 60 + 14 - SB - SG - 14 - SGB

Can anyone provide links to some problems to use this stuff on? I think it's a very quick way to solve these types fo problems, but it would certainly help to have some practice problems.

hope this helps someone.
_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Re: Set Theory - A new perspective...maybe. [#permalink]

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08 Aug 2008, 09:04

Jallen, Do you know any book with good Set theory and statistics fundamentals? And I am very poor in number theory and Inequalities. Any tips how to improve? thanks
_________________

Re: Set Theory - A new perspective...maybe. [#permalink]

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08 Aug 2008, 09:47

Allen, Thanks for starting this thread. I also had the same problem. I can solve the set/venn diagram problems (2D or 3D) using the diagramming method, however, it takes a long time compared to this plug in formula method.

Also, one other area I want to improve on is the the "mixture" problems. DO we have a thread that talks about solving those types of problems? Does anybody have any links for practicing those type of problems?
_________________

To find what you seek in the road of life, the best proverb of all is that which says: "Leave no stone unturned." -Edward Bulwer Lytton

Re: Set Theory - A new perspective...maybe. [#permalink]

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09 Aug 2008, 21:16

allen, Have u heard this problem .? Let us try this one. See if we can get it solved without any visual diagrams.

There is a shortage of tubelights, bulbs and fans in a village. It is found that • All houses do not have either tubelight or bulb or fan. • exactly 19% of houses do not have just one of these. • atleast 67% of houses do not have tubelights. • atleast 83% of houses do not have bulbs. • atleast 73% of houses do not have fans. What percentage of houses have (i) all three items tubelight, bulb and fan missing? (ii)exactly 2 items missing?

Re: Set Theory - A new perspective...maybe. [#permalink]

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09 Aug 2008, 23:02

chan4312 wrote:

allen, Have u heard this problem .? Let us try this one. See if we can get it solved without any visual diagrams.

There is a shortage of tubelights, bulbs and fans in a village. It is found that • All houses do not have either tubelight or bulb or fan. • exactly 19% of houses do not have just one of these. • atleast 67% of houses do not have tubelights. • atleast 83% of houses do not have bulbs. • atleast 73% of houses do not have fans. What percentage of houses have (i) all three items tubelight, bulb and fan missing? (ii)exactly 2 items missing?

I think there is something wrong with the words used. If you use "at least 67%" that doesn't tell me anything. It could be 100% of houses do not have tubelights because 100% is at least 67%. I don't think it can be answered definitively as written.
_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Re: Set Theory - A new perspective...maybe. [#permalink]

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10 Aug 2008, 20:09

jallenmorris wrote:

chan4312 wrote:

allen, Have u heard this problem .? Let us try this one. See if we can get it solved without any visual diagrams.

There is a shortage of tubelights, bulbs and fans in a village. It is found that • All houses do not have either tubelight or bulb or fan. • exactly 19% of houses do not have just one of these. • atleast 67% of houses do not have tubelights. • atleast 83% of houses do not have bulbs. • atleast 73% of houses do not have fans. What percentage of houses have (i) all three items tubelight, bulb and fan missing? (ii)exactly 2 items missing?

I think there is something wrong with the words used. If you use "at least 67%" that doesn't tell me anything. It could be 100% of houses do not have tubelights because 100% is at least 67%. I don't think it can be answered definitively as written.

Nope. There is no verbiage error here. Let us start this way..Assume Every house in the village has all the three items tubelight, bulb and fan. Now based on the given data , eliminate all possible exceptions to the above assumption. 19% of them do not have just one of the three.So remove 19 items from the total.

Re: Set Theory - A new perspective...maybe. [#permalink]

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10 Aug 2008, 21:08

chan4312 wrote:

jallenmorris wrote:

chan4312 wrote:

allen, Have u heard this problem .? Let us try this one. See if we can get it solved without any visual diagrams.

There is a shortage of tubelights, bulbs and fans in a village. It is found that • All houses do not have either tubelight or bulb or fan. • exactly 19% of houses do not have just one of these. • atleast 67% of houses do not have tubelights. • atleast 83% of houses do not have bulbs. • atleast 73% of houses do not have fans. What percentage of houses have (i) all three items tubelight, bulb and fan missing? (ii)exactly 2 items missing?

I think there is something wrong with the words used. If you use "at least 67%" that doesn't tell me anything. It could be 100% of houses do not have tubelights because 100% is at least 67%. I don't think it can be answered definitively as written.

Nope. There is no verbiage error here. Let us start this way..Assume Every house in the village has all the three items tubelight, bulb and fan. Now based on the given data , eliminate all possible exceptions to the above assumption. 19% of them do not have just one of the three.So remove 19 items from the total.

I have the solution..will post in 2 days.

I have to agree with jallen, something doesn't seem right with this question - unless I'm just blanking... which is also possible.

For example, if I say 81% of them have no items (and at least 2% has just bulbs missing), then it matches all conditions you've given. If I say 80% of them have no items (and at least 3% has jus bulbs missing), it still matches all conditions you've given, no?

Re: Set Theory - A new perspective...maybe. [#permalink]

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12 Aug 2008, 06:22

chan4312 wrote:

jallenmorris wrote:

chan4312 wrote:

allen, Have u heard this problem .? Let us try this one. See if we can get it solved without any visual diagrams.

There is a shortage of tubelights, bulbs and fans in a village. It is found that • All houses do not have either tubelight or bulb or fan. • exactly 19% of houses do not have just one of these. • atleast 67% of houses do not have tubelights. • atleast 83% of houses do not have bulbs. • atleast 73% of houses do not have fans. What percentage of houses have (i) all three items tubelight, bulb and fan missing? (ii)exactly 2 items missing?

I think there is something wrong with the words used. If you use "at least 67%" that doesn't tell me anything. It could be 100% of houses do not have tubelights because 100% is at least 67%. I don't think it can be answered definitively as written.

Nope. There is no verbiage error here. Let us start this way..Assume Every house in the village has all the three items tubelight, bulb and fan. Now based on the given data , eliminate all possible exceptions to the above assumption. 19% of them do not have just one of the three.So remove 19 items from the total.

I have the solution..will post in 2 days.

Ok here it comes. Let us assume that there are 100 houses in the village..So Assume that all 100 houses have tubelights, bulbs and fans. So that would be 300 items there.

we know that there is shortage of atleast (67+83+73) 223 items in every 100 houses.

Given that exactly 19% of houses do not have just one of those 3 items , we can remove 19 items from the total..Now we account for 204 missing items in 81 houses... right.! So 81 houses are missing exactly 2 items or all missing. If 81 houses are missing all 3 items then total missing items will be 81*3=243 But we only have 204 missing items. So 81 houses missing 2 items each will account for 81*2=162 items missing .

204 - 162= 42 missed items left over. So 42 items are missing means 42% houses do not have all the three items.

I got this question and its solution online. I did not solve it.

Re: Set Theory - A new perspective...maybe. [#permalink]

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12 Aug 2008, 06:30

what's the source of this question? the wording is strange and it's wording that you'd never see on a real GMAT question "do not have just" makes me think it was certainly not written by GMAT authors.

The wording is confusing and you can't really tell what the question is asking.

"All houses do not have either tubelight or bulb or fan."

What does this really mean? Is "do not have" supposed to mean missing or non-working? Does it mean the house never had one or more of these items to begin with. It makes me think that the authors of this intended "do not have" to mean "missing" or "not working" but that's a meaning that isn't clear. "do not have" is usually used with regard to possession. Such as "I do not have a dog." It seems like with the way the phrase is used here, the authors mean the dog is missing, which implies that I had a dog to begin with. The phrase "I do not have a dog." does not support the assumption that I did have a dog but now I do not have one becuase the dog is missing. Same idea applies here. If the houses do not have either tubelights, bulb, or fan, that does not mean the houses DID have one but now they are missing or not working.

I think this is a very poorly written question.
_________________

------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

Re: Set Theory - A new perspective...maybe. [#permalink]

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12 Aug 2008, 06:38

Sonics is gone man.! Get over it..

In case you didn't see where I'm from, I living in Oklahoma City. We're the team GETTING the Sonics franchise and I couldn't be happier. There is nothing to get over.

Re: Set Theory - A new perspective...maybe. [#permalink]

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12 Aug 2008, 06:45

Well that is great. I did not notice that. Kevin Durant is here Reading that the Sonics don't live in Seattle anymore: Priceless.

Should not this be like this ? Reading that the Sonics coming to Oklahoma : Priceless.

Well anyway ...Houses don't have those items. it does not mean they are broken. They are not present. Those might be using some other things. a house may be missing 1 , 2 or 3 items.