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

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: https://www.youtube.com/watch?v=uE_aMa_W0o0

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.

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.

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.

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

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}.

Hope it's clear.

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.

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

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

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.

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

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

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