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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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13 Aug 2007, 04:16
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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?

I. One-half of the guests had a house in Palm Beach.

II. Two-thirds of the guests had a house in the Hamptons

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13 Aug 2007, 07:07
AugiTh wrote:
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?

I. One-half of the guests had a house in Palm Beach.

II. Two-thirds of the guests had a house in the Hamptons

both statements are together sufficient but not alone.

I. Palm Beach house: 180/2 or 90 guests have but still we do not know how many of them have house in Hamptons. not suff

II. Hamptons house: 180*(2/3) or 120 has house in Hamptons. we still do not know how many of those guys have houses in Palm Beach. not alone suff.

I+II. since at least 90 guys have houses in Palm Beach and 120 guys have houses in Hampton. now we can construct a vien diagram and get the solution.
so both statements taken together suff. not alone
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13 Aug 2007, 09:47
One question: How many guests in the party: 180???
Cause it say 180 of the guest.
I choose E.
Director
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13 Aug 2007, 12:07
No way to tell. E is the answer.

They say 180 of the guests have both but not all the guests have either one. There is no way to tell the number of people or where there is overlap in segments.
Manager
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13 Aug 2007, 12:34
No way to find out what the ratio of (PB but not H)/(H but not PB)

What we are able to find out is the ratio of the total PB/H which is 4PB=3H, but that does not help.

Senior Manager
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26 Oct 2009, 04:38
Isn't the formula:

ALL members = Hamptons + Palm Beach - H&P
Total = 1/2 total + 2/3 of total - 180

x = 1/2 x + 2/3 x - 180
we can solve for x

Can someone explain what is wrong with this approach.

Thanks
Re: Charity fundraiser   [#permalink] 26 Oct 2009, 04:38
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