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At a charity fundraiser, 180 of the guests had a house both

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At a charity fundraiser, 180 of the guests had a house both [#permalink] New post 20 Apr 2012, 16:36
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At a charity fundraiser, 180 of the guests had a house both in the Hamptons and in Palm Beach. If not everyone at the fundraiser had a house in either the Hamptons or Palm Beach, what is the ratio of the number of people who had a house in Palm Beach but not in the Hamptons to the number of people who had a house in the Hamptons but not in Palm Beach?

(1) One-half of the guests had a house in Palm Beach.
(2) Two-thirds of the guests had a house in the Hamptons
[Reveal] Spoiler: OA

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Re: House in the Hamptons [#permalink] New post 20 Apr 2012, 16:39
I dont get why the answer is E and not C.
It is given to use that all guests had a house in either the hamptons or palm beach.
with that info we can use stmt 1 and say 1/2 the guest had a house in the hampton but not in pb and then with stmt 2 we have 1/3 of the guests had a house in PB but not in hamptons
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Re: House in the Hamptons [#permalink] New post 20 Apr 2012, 23:41
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calreg11 wrote:
I dont get why the answer is E and not C.
It is given to use that all guests had a house in either the hamptons or palm beach.
with that info we can use stmt 1 and say 1/2 the guest had a house in the hampton but not in pb and then with stmt 2 we have 1/3 of the guests had a house in PB but not in hamptons


Actually exactly the opposite of this is given: "NOT everyone at the fundraiser had a house in either the Hamptons or Palm Beach"

At a charity fundraiser, 180 of the guests had a house both in the Hamptons and in Palm Beach. If not everyone at the fundraiser had a house in either the Hamptons or Palm Beach, what is the ratio of the number of people who had a house in Palm Beach but not in the Hamptons to the number of people who had a house in the Hamptons but not in Palm Beach?

(1) One-half of the guests had a house in Palm Beach.
(2) Two-thirds of the guests had a house in the Hamptons

Look at the diagram below for (1)+(2):
Attachment:
Houses.png
Houses.png [ 8.36 KiB | Viewed 2672 times ]

We should find the ratio of yellow boxes, but with the info given it's not possible.

Answer: E.

Hope it helps.
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Re: House in the Hamptons [#permalink] New post 21 Apr 2012, 02:19
Bunuel wrote:
calreg11 wrote:
I dont get why the answer is E and not C.
It is given to use that all guests had a house in either the hamptons or palm beach.
with that info we can use stmt 1 and say 1/2 the guest had a house in the hampton but not in pb and then with stmt 2 we have 1/3 of the guests had a house in PB but not in hamptons


Actually exactly the opposite of this is given: "NOT everyone at the fundraiser had a house in either the Hamptons or Palm Beach"

At a charity fundraiser, 180 of the guests had a house both in the Hamptons and in Palm Beach. If not everyone at the fundraiser had a house in either the Hamptons or Palm Beach, what is the ratio of the number of people who had a house in Palm Beach but not in the Hamptons to the number of people who had a house in the Hamptons but not in Palm Beach?

(1) One-half of the guests had a house in Palm Beach.
(2) Two-thirds of the guests had a house in the Hamptons

Look at the diagram below for (1)+(2):
Attachment:
Houses.png

We should find the ratio of yellow boxes, but with the info given it's not possible.

Answer: E.

Hope it helps.


Hi Bunuel, a small doubt.

Why isn't the value in first row and first column i.e House in Palm Beach and House in Hamptons equal to 180?
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Re: House in the Hamptons [#permalink] New post 21 Apr 2012, 02:26
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sei wrote:
Hi Bunuel, a small doubt.

Why isn't the value in first row and first column i.e House in Palm Beach and House in Hamptons equal to 180?


Why should they? It's seems that you are not comfortable with a double set matrix, this might help: http://www.youtube.com/watch?v=uE_aMa_W0o0
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Re: House in the Hamptons [#permalink] New post 21 Apr 2012, 04:17
Bunuel wrote:
sei wrote:
Hi Bunuel, a small doubt.

Why isn't the value in first row and first column i.e House in Palm Beach and House in Hamptons equal to 180?


Why should they? It's seems that you are not comfortable with a double set matrix, this might help


Thank you very very much for the video link. :)

But I am still confused with regards to the answer given by you.

Please see attachment.

The language in the question - 180 of the guests had a house both in the Hamptons and in Palm Beach. Doesn't it seem to be the same as saying - there were 9 green trucks in the youtube example that you gave?
Attachments

cars.PNG
cars.PNG [ 89.27 KiB | Viewed 2697 times ]

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Re: House in the Hamptons [#permalink] New post 21 Apr 2012, 10:28
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sei wrote:
Bunuel wrote:
sei wrote:
Hi Bunuel, a small doubt.

Why isn't the value in first row and first column i.e House in Palm Beach and House in Hamptons equal to 180?


Why should they? It's seems that you are not comfortable with a double set matrix, this might help


Thank you very very much for the video link. :)

But I am still confused with regards to the answer given by you.

Please see attachment.

The language in the question - 180 of the guests had a house both in the Hamptons and in Palm Beach. Doesn't it seem to be the same as saying - there were 9 green trucks in the youtube example that you gave?


I filled the entire matrix above (there was a typo, which is now edited). Hope it's clear now.
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Re: House in the Hamptons [#permalink] New post 01 Oct 2012, 19:28
Hello Bunuel,

How do we know the ratio of the two in yellow cells is not solvable by just looking at it? I actually tried solving and of course got stuck at it but I thought because there is one degree of x in the equation it might actually lead to a ratio. How did you know it was unsolvable algebraically by just looking at it? Thank you in advance.

Bunuel wrote:
calreg11 wrote:
I dont get why the answer is E and not C.
It is given to use that all guests had a house in either the hamptons or palm beach.
with that info we can use stmt 1 and say 1/2 the guest had a house in the hampton but not in pb and then with stmt 2 we have 1/3 of the guests had a house in PB but not in hamptons


Actually exactly the opposite of this is given: "NOT everyone at the fundraiser had a house in either the Hamptons or Palm Beach"

At a charity fundraiser, 180 of the guests had a house both in the Hamptons and in Palm Beach. If not everyone at the fundraiser had a house in either the Hamptons or Palm Beach, what is the ratio of the number of people who had a house in Palm Beach but not in the Hamptons to the number of people who had a house in the Hamptons but not in Palm Beach?

(1) One-half of the guests had a house in Palm Beach.
(2) Two-thirds of the guests had a house in the Hamptons

Look at the diagram below for (1)+(2):
Attachment:
Houses.png

We should find the ratio of yellow boxes, but with the info given it's not possible.

Answer: E.

Hope it helps.
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Re: House in the Hamptons [#permalink] New post 02 Oct 2012, 01:32
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minkathebest wrote:
Hello Bunuel,

How do we know the ratio of the two in yellow cells is not solvable by just looking at it? I actually tried solving and of course got stuck at it but I thought because there is one degree of x in the equation it might actually lead to a ratio. How did you know it was unsolvable algebraically by just looking at it? Thank you in advance.


Well, as you can see in the matrix all boxes are filled and we still have x in both of them which do not cancel when we make the ratio.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: At a charity fundraiser, 180 of the guests had a house both [#permalink] New post 06 Oct 2012, 06:12
Hi Bunuel!

the question can be solved better though venn diagram.

and answer would be "E" because neither total is given nor only Hampton houses or only palm beach houses are given.
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Re: House in the Hamptons [#permalink] New post 30 Nov 2012, 03:24
Bunuel wrote:
calreg11 wrote:
I dont get why the answer is E and not C.
It is given to use that all guests had a house in either the hamptons or palm beach.
with that info we can use stmt 1 and say 1/2 the guest had a house in the hampton but not in pb and then with stmt 2 we have 1/3 of the guests had a house in PB but not in hamptons


Actually exactly the opposite of this is given: "NOT everyone at the fundraiser had a house in either the Hamptons or Palm Beach"

At a charity fundraiser, 180 of the guests had a house both in the Hamptons and in Palm Beach. If not everyone at the fundraiser had a house in either the Hamptons or Palm Beach, what is the ratio of the number of people who had a house in Palm Beach but not in the Hamptons to the number of people who had a house in the Hamptons but not in Palm Beach?

(1) One-half of the guests had a house in Palm Beach.
(2) Two-thirds of the guests had a house in the Hamptons

Look at the diagram below for (1)+(2):
Attachment:
Houses.png

We should find the ratio of yellow boxes, but with the info given it's not possible.

Answer: E.

Hope it helps.



Bunuel you nail the question in the easiest way possible. I had already visited all the forums possible, was about to give up on my doubt till i found your explanation. You are the Best!!!!!!!!!!!!!!!
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Re: At a charity fundraiser, 180 of the guests had a house both [#permalink] New post 22 May 2014, 23:57
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Re: At a charity fundraiser, 180 of the guests had a house both   [#permalink] 22 May 2014, 23:57
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