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

Question

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

Show Answer

Official Answer

E

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

Bunuel · Accepted Answer

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.

calreg11 · Answer

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

sei · Answer

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?

Bunuel · Answer

Why should they? It's seems that you are not comfortable with a double set matrix, this might help: https://www.youtube.com/watch?v=uE_aMa_W0o0

sei · Answer

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?

Bunuel · Answer

I filled the entire matrix above (there was a typo, which is now edited). Hope it's clear now.

minkathebest · Answer

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 · Answer

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.

leaderz · Answer

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.

Mbawarrior01 · Answer

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!!!!!!!!!!!!!!!

logophobic · Answer

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...

Bunuel · 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.

wikdwik · Answer

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.

tinnyshenoy · Answer

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

Bunuel · Answer

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

tinnyshenoy · Answer

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?

Thanks for your reply.

prajwalgote · Answer

Hi,

The question only asks for the ratio. Then we can surely get a ratio without further solving for it.

Confused ......why not "C"...

Thanks
Prajwal

randomavoidplease · Answer

I too made that mistake, when I read the prompt and glanced over the statements, Because no of total of house guests is not given, nor any other specific information about the guests except for total number of guests who have a house in BOTH. And I thought to myself, the answer has to be "E".

But thought lets solve, I believe the trickry was in the solving of things. Because variables aligned I started thinking hold on it can be solved but needed both statements. As it turns out my first instinct was right and I picked C which was wrong.

I don't know if it helps or not, or maybe I was completely wrong. Do let me know though, if my instinct was correct or not.

Thanks

bumpbot · Answer

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

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