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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]  10 Aug 2008, 15:02
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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

For this question "If not everyone at the fundraiser had a house in either the Hamptons or Palm Beach" does this sentence not mean that everyone has a house either in the Hamptions or Palm Beach. So when you draw your grid the No Hamptons and No Palm Beach should be 0". However, in the explanation the answer is different.
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Re: GRID PRoblem [#permalink]  10 Aug 2008, 17:16
I think C.
When it says that not every visitor had a house in PB or Hampton, it means the total of house owners is < 180. It does not say that no one had a house at both places. So intersection is not 0.

But that does not affect our solution. We are asked to find only the ratio x:y not the actual values. so we should be fine

Draw a venn diagram. Say Palm beach alone = x hampton alone = y and both =z

x+y+z =T.

required : x/y

1) says half the ppl had house in palm beach. so x+z=T/2. so y=T/2. not sufficient to get the ration x/y

2) says two thirds had a house in hampton. so y+z = 2T/3. so x=T/3 again not sufficient to get x/y

combine 1 and 2 and we get x/y = 2/3
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Re: GRID PRoblem [#permalink]  10 Aug 2008, 19:01
i wouldve said E ...
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Re: GRID PRoblem [#permalink]  10 Aug 2008, 20:38
x97agarwal 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?

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

(2) Two-thirds of the guests had a house in the Hamptons

For this question "If not everyone at the fundraiser had a house in either the Hamptons or Palm Beach" does this sentence not mean that everyone has a house either in the Hamptions or Palm Beach. So when you draw your grid the No Hamptons and No Palm Beach should be 0". However, in the explanation the answer is different.

"If not everyone at the fundraiser had a house in either the Hamptons or Palm Beach"
---> means there are some guests who doesn't have house in either Haptons or Palm Beach.

for e.g

100 people had a house in H or P beach.
not 100 people had a house in H or P beach.. ---> means there may be few people don't have house in H or P beach.

------H ------- P ----- Both H & P ---- No House in H or P
1)-----?? ----- (1/2)x---- 180 ---------- ??
2)-----(2/3)x---??--------180 ----------- ??

1) IS NOT SUFFCIENT we don't know about H houses count

2) is not suffcieint we don't knwo about P houses count

combined
required ratio= ((1/2)x -180)/((2/3)x-180)
==??? we don't the values of x

Will go for E
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Re: GRID PRoblem [#permalink]  10 Aug 2008, 22:21
x97agarwal wrote:
For this question "If not everyone at the fundraiser had a house in either the Hamptons or Palm Beach" does this sentence not mean that everyone has a house either in the Hamptions or Palm Beach. So when you draw your grid the No Hamptons and No Palm Beach should be 0". However, in the explanation the answer is different.

this means "not all had a house (in either place)".

opt for E.
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Re: GRID PRoblem [#permalink]  11 Aug 2008, 00:09
For "If not everyone at the fundraiser had a house in either the Hamptons or Palm Beach",

“not everyone had a house in either the Hamptons or Plam Beach” mean “someone do not have a house in either the two places. So in the grid, the non-Hamptons-and-non-Palm-Beach should not be zero.

…………….. lll Ham lll non-Ham lll Total
Palm Beach lll 180 lll B lll 180+B
Non- Palm lll C lll D lll C+D
Total ………….lll 180+C lll B+D lll 180+B+C+D

D > 0

Find B/C

(1) tells us:
180+B = (180+B+C+D)/2
360+2B=180+B+C+D
180+B=C+D ------- (i)

no more info is given, we cannot find the ratio of B to C

(2) tell us
180+C=(180+B+C+D)*2/3
540+3C=360+2B+2C+2D
180+C=2B+2D ---------- (ii)

Again, we cannot find B, hence we cannot find B/C

(1) & (2)
We can try to eliminate D, (i)*2 – (ii)
360+2B-180-C=2C+2D-2B-2D
180+2B-C=2C+2B
3C=180
C=60
But still we cannot get B

So Ans is E
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Re: GRID PRoblem [#permalink]  11 Aug 2008, 06:55
x97agarwal 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?

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

(2) Two-thirds of the guests had a house in the Hamptons

For this question "If not everyone at the fundraiser had a house in either the Hamptons or Palm Beach" does this sentence not mean that everyone has a house either in the Hamptions or Palm Beach. So when you draw your grid the No Hamptons and No Palm Beach should be 0". However, in the explanation the answer is different.

PALM 1/2 x

HAMPTON 2/3 x

where x is total number of guests. ok
Now Let us find out number of guests who have homes in both beaches.That means
2/3 x - 1/2 x = 1/6 x

So Ratios = ( 1/2 x - 1/6 x ) / 1/6 x
= (1/3) / (1/6)
= 2/1

So IMO C
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Re: GRID PRoblem [#permalink]  11 Aug 2008, 08:30
bhushangiri wrote:
judokan wrote:
bhushangiri wrote:
x+y+z =T.
x+y+z+a = T , a is the numbers of people having houses neither in PB nor in hampton

But we don't need a. The required ratio is between x and y - Only house owners. So non owners are not even required.

Also, you don't need 180 figure. That data is redundant since we are only required to find the ratio x:y.

You would require a because total guests do contain guests which do not have houses in both
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Re: GRID PRoblem [#permalink]  11 Aug 2008, 09:00
All right folks.. my bad. I read the question wrong and have been solving it incorrectly for each of my previous posts.
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Re: GRID PRoblem [#permalink]  11 Aug 2008, 09:26
Total Guests = H + P + (H+P) + Neither.

You can't solve this without knowing Neither. Therefore E.
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Re: GRID PRoblem [#permalink]  12 Aug 2008, 06:47
x97agarwal 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?

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

For this question "If not everyone at the fundraiser had a house in either the Hamptons or Palm Beach" does this sentence not mean that everyone has a house either in the Hamptions or Palm Beach. So when you draw your grid the No Hamptons and No Palm Beach should be 0". However, in the explanation the answer is different.

Total number of people in the fundraising program = T
the number of people who had a house both in the Hamptons and in Palm Beach = P&H = 180

the number of people who had a house in Palm Beach = P
the number of people who had a house in Palm Beach but not in the Hamptons = P (not H)
so, P = 180 + P (not H)

the number of people who had a house in the Hamptons = H
the number of people who had a house in the Hamptons but not in Palm Beach = H (not P)
so, H = 180 + H (not P)

the number of people who had no house either in the Hamptons or in Palm Beach = P&H (not)
so, total = T = 180 + P (not H) + H (not P) + P&H (not)

The question is: what is 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?
or, what is P (not H) / H (not P) = ?

(1) One-half of the guests had a house in Palm Beach.
P = T/2
180 + P (not H) = (180 + P (not H) + H (not P) + P&H (not))/2
180 + P (not H) = H (not P) + P&H (not)
180 = H (not P) + P&H (not) - P (not H) ............................(i)

nsf.........

(2) Two-thirds of the guests had a house in the Hamptons

H = 2T/3
3H = 2T
3 (180 + H (not P)) = 2 (180 + P (not H) + H (not P) + P&H (not))
180 + H (not P) = 2 (P (not H)) + 2(P&H (not))
180 = 2 (P (not H)) + 2(P&H (not)) - H (not P) ........................... (ii)

nsf.........

from 1 and 2, i and ii are equal. so

H (not P) + P&H (not) - P (not H) = 2 (P (not H)) + 2(P&H (not)) - H (not P)
2 (H (not P)) = P&H (not) + 3 (P (not H))

since we do not know awhat is P&H (not), still insufficient. E.
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Re: GRID PRoblem   [#permalink] 12 Aug 2008, 06:47
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