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At a charity fundraiser, 180 of the guests had a house both [#permalink]
20 Apr 2012, 16:36

1

This post received KUDOS

3

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

66% (02:32) correct
34% (01:47) wrong based on 192 sessions

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

Re: House in the Hamptons [#permalink]
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 _________________

Re: House in the Hamptons [#permalink]
20 Apr 2012, 23:41

2

This post received KUDOS

Expert's post

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 [ 8.36 KiB | Viewed 4019 times ]

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

Re: House in the Hamptons [#permalink]
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?

Re: House in the Hamptons [#permalink]
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?

Re: House in the Hamptons [#permalink]
21 Apr 2012, 10:28

1

This post received KUDOS

Expert's post

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. _________________

Re: House in the Hamptons [#permalink]
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.

Re: House in the Hamptons [#permalink]
02 Oct 2012, 01:32

Expert's post

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. _________________

Re: House in the Hamptons [#permalink]
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!!!!!!!!!!!!!!!

Re: At a charity fundraiser, 180 of the guests had a house both [#permalink]
22 May 2014, 23:57

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

Re: At a charity fundraiser, 180 of the guests had a house both [#permalink]
07 Sep 2014, 07:52

1

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

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}.

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