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# In a certain club, every member likes red wine or white wine

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In a certain club, every member likes red wine or white wine [#permalink]

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24 Jun 2012, 03:43
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Difficulty:

95% (hard)

Question Stats:

41% (02:47) correct 59% (01:40) wrong based on 504 sessions

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In a certain club, every member likes red wine or white wine or both. If the number of club members that like red wine and do not like white wine is three times the number of club members that like white wine and do not like red wine, then what is the number of club members that like both red wine and white wine?

(1) The total number of club members is 60.

(2) The number of club members that do not like white wine is three times that number of club members that do like white wine.
[Reveal] Spoiler: OA
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Re: In a certain club, every member likes red wine or white wine [#permalink]

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24 Jun 2012, 04:10
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In a certain club, every member likes red wine or white wine or both. If the number of club members that like red wine and do not like white wine is three times the number of club members that like white wine and do not like red wine, then what is the number of club members that like both red wine and white wine?

Since in the club every member likes red wine or white wine or both, then there are no members who like neither of the wines, so we have that:
{Total}={Red}+{White}-{Both}.

Also given that {Red}-{Both}=3*({White}-{Both}) --> {Red}=3*{White}-2*{Both}. So, {Total}=(3*{White}-2{Both})+{White}-{Both} --> {Total}=4*{White}-3*{Both}

(1) The total number of club members is 60 --> 60=4*{White}-3*{Both}. Two unknowns. Not sufficient.

(2) The number of club members that do not like white wine is three times that number of club members that do like white wine --> {Total}-{White}=3*{White} --> {Total}=4*{White}. So, 4*{White}=4*{White}-3*{Both} --> 3*{Both}=0 --> {Both}=0. Sufficient.

Hope it's clear.
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Re: In a certain club, every member likes red wine or white wine [#permalink]

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10 Aug 2012, 16:19
Bunuel wrote:
In a certain club, every member likes red wine or white wine or both. If the number of club members that like red wine and do not like white wine is three times the number of club members that like white wine and do not like red wine, then what is the number of club members that like both red wine and white wine?

Since in the club every member likes red wine or white wine or both, then there are no members who like neither of the wines, so we have that:
{Total}={Red}+{White}-{Both}.

Also given that {Red}-{Both}=3*({White}-{Both}) --> {Red}=3*{White}-2*{Both}. So, {Total}=(3*{White}-2{Both})+{White}-{Both} --> {Total}=4*{White}-3*{Both}

(1) The total number of club members is 60 --> 60=4*{White}-3*{Both}. Two unknowns. Not sufficient.

(2) The number of club members that do not like white wine is three times that number of club members that do like white wine --> {Total}-{White}=3*{White} --> {Total}=4*{White}. So, 4*{White}=4*{White}-3*{Both} --> 3*{Both}=0 --> {Both}=0. Sufficient.

Hope it's clear.

Doing the set matrix:

------------ red---- not red--- tot
white -------- ? ------ x
not white ---- 3x ------ 0
tot

2)
------------ red---- not red--- tot
white -------- ? ------ x ------ y
not white ---- 3x ----- 0 ----- 3y
tot

So, y=x. and this implies white/red = 0

Is this the right reasoning?
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Posts: 39702
Re: In a certain club, every member likes red wine or white wine [#permalink]

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11 Aug 2012, 00:54
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Expert's post
superpus07 wrote:
Bunuel wrote:
In a certain club, every member likes red wine or white wine or both. If the number of club members that like red wine and do not like white wine is three times the number of club members that like white wine and do not like red wine, then what is the number of club members that like both red wine and white wine?

Since in the club every member likes red wine or white wine or both, then there are no members who like neither of the wines, so we have that:
{Total}={Red}+{White}-{Both}.

Also given that {Red}-{Both}=3*({White}-{Both}) --> {Red}=3*{White}-2*{Both}. So, {Total}=(3*{White}-2{Both})+{White}-{Both} --> {Total}=4*{White}-3*{Both}

(1) The total number of club members is 60 --> 60=4*{White}-3*{Both}. Two unknowns. Not sufficient.

(2) The number of club members that do not like white wine is three times that number of club members that do like white wine --> {Total}-{White}=3*{White} --> {Total}=4*{White}. So, 4*{White}=4*{White}-3*{Both} --> 3*{Both}=0 --> {Both}=0. Sufficient.

Hope it's clear.

Doing the set matrix:

------------ red---- not red--- tot
white -------- ? ------ x
not white ---- 3x ------ 0
tot

2)
------------ red---- not red--- tot
white -------- ? ------ x ------ y
not white ---- 3x ----- 0 ----- 3y
tot

So, y=x. and this implies white/red = 0

Is this the right reasoning?

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Re: In a certain club, every member likes red wine or white wine [#permalink]

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12 Aug 2012, 10:42
manulath wrote:

(2) The number of club members that do not like white wine is three times that number of club members that do like white wine.

--x--
Ah, i failed to carefully read (2) where it says at the end "..number of club members that do like white wine", which is the sum of those who like Both + those who like only like White wine (as opposed to those who only like white)
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Re: In a certain club, every member likes red wine or white wine [#permalink]

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16 Sep 2012, 06:59
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Let a --> no of ppl who like Red wine alone
c -->no of ppl who like white wine alone
b --> no of ppl who like both

from the question a=3c and we have to find b

1) a+b+c = 60.. nothing can be inferred abt b
2) a=3(b+c)

and from the question we know a=3c which implies b=0

hence 2 alone is sufficient
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Re: In a certain club, every member likes red wine or white wine [#permalink]

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15 Jul 2013, 00:42
From 100 hardest questions
Bumping for review and further discussion.
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Re: In a certain club, every member likes red wine or white wine [#permalink]

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22 Jul 2014, 09:44
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In a certain club, every member likes red wine or white wine [#permalink]

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25 Sep 2015, 23:22
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In a certain club, every member likes red wine or white wine [#permalink]

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30 Oct 2016, 02:52
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: In a certain club, every member likes red wine or white wine   [#permalink] 30 Oct 2016, 02:52
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