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12 Feb 2021, 01:15
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B
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Difficulty:
95%
(hard)
Question Stats:
39% (02:16) correct
61%
(02:19)
wrong
based on 157
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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.
(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.
15 Feb 2021, 01:30
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Bunuel
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}
The question is asks about {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.
Answer: B.
Hope it's clear.
General Discussion
12 Feb 2021, 03:28
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The answer will be B.
Posted from my mobile device
Posted from my mobile device
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