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

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Manager
Joined: 12 May 2012
Posts: 80

Kudos [?]: 120 [4], given: 14

Location: India
Concentration: General Management, Operations
GMAT 1: 650 Q51 V25
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WE: General Management (Transportation)
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% (01:45) correct 59% (01:38) wrong based on 525 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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Math Expert
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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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Kudos [?]: 132772 [1], given: 12372

Intern
Joined: 20 Jun 2011
Posts: 46

Kudos [?]: 119 [0], given: 1

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?

Kudos [?]: 119 [0], given: 1

Math Expert
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Posts: 42264

Kudos [?]: 132772 [1], given: 12372

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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Kudos [?]: 132772 [1], given: 12372

Senior Manager
Joined: 15 May 2011
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WE: Research (Consulting)
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
2
KUDOS
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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30 Oct 2016, 02:52
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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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