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

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Joined: 29 Jan 2005
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At a charity fundraiser, 180 of the guests had a house both [#permalink]  18 Dec 2005, 01:12
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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
Director
Joined: 17 Dec 2005
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Location: Germany
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[#permalink]  18 Dec 2005, 04:50
Hey,

I think it's C, because

We want to know the ratio of the people who have a house only in Palm Beach to those who have only one in Hamptons.

Let's take some notes:

A= Hamptons
B= Palm Beach
A a B= both

We know A a B= 180

and A + B + A a B= E (all members, since the questions does not suggest any homeless members)

(1) B= 1/2 E
(2) A= 2/3 E

Both alone are insufficiant, since they provide three too less information, but together it becomes clear that the people who have just one house are 5/6 of the entire club, because 1/2 + 2/3= 5/6, thus

The 180 people who own two houses make up 1/6, theefore the entire club has 1080members, thus 540 people who have soleyly one house in B and 720 who have just one house in A.

Rate= 720/540
Manager
Joined: 02 Jun 2005
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Re: DS MGMAT 1-4 [#permalink]  18 Dec 2005, 09:52
GMATT73 wrote:
If not everyone at the fundraiser had a house in either the Hamptons or Palm Beach,...

Does the above sentence suggest that there are some people do not have houses on either Hamptons or Palm Beach at all?
Re: DS MGMAT 1-4   [#permalink] 18 Dec 2005, 09:52
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# At a charity fundraiser, 180 of the guests had a house both

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