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nahid078: Master | Next Rank: 500 Posts; Posts: 105; Joined: Tue May 13, 2014 10:41 am; Thanked: 2 times; Followed by:1 members

wine

by nahid078 » Fri Jul 03, 2015 9:16 am

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.

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Source: Beat The GMAT — Data Sufficiency | Fri Jul 03, 2015 9:16 am

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 am; Location: Montreal; Thanked: 1090 times; Followed by:355 members; GMAT Score:780

by Ian Stewart » Fri Jul 03, 2015 10:34 am

We can draw a Venn diagram, with one circle for people who like red wine, and one for people who like white wine. If x people like only white wine, the question tells us 3x people like only red wine. So our Venn has the following zones, using 'b' for the number who like both:

like only red: 3x
like both: b
like only white: x

Statement 1 is not sufficient - it tells us that the sum of the three values above is 60, but you'll have different values for b if you change the value of x.

Statement 2 talks about "the number of members who do not like white wine". That's just the number who like only red wine, so is just 3x. Statement 2 tells us this is 3 times the number who "do like white wine", which is just the sum of those who like both wines, and those who like only white wine. So, as we can see in our Venn diagram, b + x people in total like white wine. So Statement 2 is just telling us that:

3x = 3(x + b)
3x = 3x + 3b
3b = 0
b = 0

and since the question asked for the value of b, Statement 2 is sufficient. The answer is B.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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nikhilgmat31: Legendary Member; Posts: 518; Joined: Tue May 12, 2015 8:25 pm; Thanked: 10 times

by nikhilgmat31 » Mon Jul 06, 2015 4:02 am

this is very surprising question.

There is no person who likes both red & white wine. But the question statement says - person like red or white or both.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Mon Jul 06, 2015 5:39 am

nikhilgmat31 wrote:this is very surprising question.

There is no person who likes both red & white wine. But the question statement says - person like red or white or both.

The "or" does not imply that every category is represented.
If I say that "all of the party attendees were male or female," that does not necessarily mean that there were any male attendees.

The main inference we can draw from "In a certain club, every member likes red wine or white wine or both" is that there are no members who like neither red wine nor white wine.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com