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

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Manager
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At a charity fundraiser, 180 of the guests had a house both  [#permalink]

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20 Apr 2012, 16:36
4
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Difficulty:

55% (hard)

Question Stats:

67% (02:31) correct 33% (02:40) wrong based on 576 sessions

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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

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At a charity fundraiser, 180 of the guests had a house both  [#permalink]

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20 Apr 2012, 23:41
6
1
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):

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

Hope it helps.

Attachment:

Houses.png [ 8.36 KiB | Viewed 12154 times ]

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Manager
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Re: House in the Hamptons  [#permalink]

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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]

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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.

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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Joined: 02 Sep 2009
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Re: House in the Hamptons  [#permalink]

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21 Apr 2012, 02:26
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]

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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.

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 [ 89.27 KiB | Viewed 11408 times ]

Math Expert
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Posts: 51100
Re: House in the Hamptons  [#permalink]

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21 Apr 2012, 10:28
1
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.

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]

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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.

Hope it helps.
Math Expert
Joined: 02 Sep 2009
Posts: 51100
Re: House in the Hamptons  [#permalink]

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02 Oct 2012, 01:32
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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Re: At a charity fundraiser, 180 of the guests had a house both  [#permalink]

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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]

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30 Nov 2012, 03:24
1
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.

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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Posts: 6
Re: At a charity fundraiser, 180 of the guests had a house both  [#permalink]

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07 Sep 2014, 07:26
I thought the answer was C...

The overlap of 2/3and 1/2 is 1/6 and we are given this is 180. From here you can figure out Hamptons & Palm Beach (540 & 720) and then take the ratio of Hamptons w/o 180 (360/540) and Palm Beach w/o 180 (540/720). The answer would then be (360/540)/(540/720). From what I understand, you don't need the number of people who don't have houses in either because the prompt doesn't ask for this info in the answer...
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Posts: 51100
Re: At a charity fundraiser, 180 of the guests had a house both  [#permalink]

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07 Sep 2014, 07:52
2
2
logophobic wrote:
I thought the answer was C...

The overlap of 2/3and 1/2 is 1/6 and we are given this is 180. From here you can figure out Hamptons & Palm Beach (540 & 720) and then take the ratio of Hamptons w/o 180 (360/540) and Palm Beach w/o 180 (540/720). The answer would then be (360/540)/(540/720). From what I understand, you don't need the number of people who don't have houses in either because the prompt doesn't ask for this info in the answer...

1/2 of the guests had a house in Palm Beach and 2/3 of the guests had a house in the Hamptons does not means that 1/6 of them had a house both in the Hamptons and in Palm Beach because the stem explicitly mentions that not everyone at the fundraiser had a house in either the Hamptons or Palm Beach.

So, we have {Total} = {Palm Beach} + {Hamptons} - {Both} + {Neither} --> {Total} = {Total}*1/2 + {Total}*2/3 - 180 + {Neither}.

You assumed (incorrectly) that we had: {Total} = {Palm Beach} + {Hamptons} - {Both} --> {Total} = {Total}*1/2 + {Total}*2/3 - 180, which you can solve for {Total}.

Hope it's clear.
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Re: At a charity fundraiser, 180 of the guests had a house both  [#permalink]

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08 Jun 2015, 12:44
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.

Hope it helps.

Hi Bunnel,

Can't we straight away use the statement ("NOT everyone at the fundraiser had a house in either the Hamptons or Palm Beach") as the Neither component

equation becomes :

Palm beach + Hampton - Both = Total - Neither
x/2 + 2/3x - 180 = x - Neither

Since Neither is not know so C is also not sufficient. Hence E is answer.

(Let me know if I am wrong.)

Regards,
Ritwik.
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Re: At a charity fundraiser, 180 of the guests had a house both  [#permalink]

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16 Mar 2016, 09:41
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.

Hope it helps.

Since the question is asking for a ratio of 2 columns, why cant we assume a value to X and find the ratio?
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Joined: 02 Sep 2009
Posts: 51100
Re: At a charity fundraiser, 180 of the guests had a house both  [#permalink]

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16 Mar 2016, 09:51
tinnyshenoy wrote:
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.

Hope it helps.

Since the question is asking for a ratio of 2 columns, why cant we assume a value to X and find the ratio?

Because for different values of x, the ratio will be different.
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Re: At a charity fundraiser, 180 of the guests had a house both  [#permalink]

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17 Mar 2016, 12:40
Bunuel wrote:
tinnyshenoy wrote:
Bunuel wrote:

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.

Hope it helps.

Since the question is asking for a ratio of 2 columns, why cant we assume a value to X and find the ratio?

Because for different values of x, the ratio will be different.

But in this question - in-a-certain-building-1-5-of-the-offices-have-both-a-window-141254.html - which also asks for the ratio of the same 2 columns , we assumed a value of x. Why not here?

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Re: At a charity fundraiser, 180 of the guests had a house both  [#permalink]

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