overlapping problem

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Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 am; Thanked: 14 times; Followed by:5 members

overlapping problem

by Mo2men » Thu Mar 23, 2017 1:59 am

A marketing company doing a survey at a local nightspot asked 44 drinkers about their alcohol preferences. 10 people said they drink only wine, while 4 people said they only drink wine and hard liquor. One-fourth of all the people said they only drink beer, and there was no one that said they only drink beer and wine. If two people each said they drink either all three types of beverage or only liquor and the rest of the people drink only beer and liquor, how many people said they drink don't drink wine?

A. 34
B. 28
C. 23
D. 20
E. 11

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Source: Beat The GMAT — Problem Solving | Thu Mar 23, 2017 1:59 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Thu Mar 23, 2017 2:38 am

Mo2men wrote:A marketing company doing a survey at a local nightspot asked 44 drinkers about their alcohol preferences. 10 people said they drink only wine, while 4 people said they only drink wine and hard liquor. One-fourth of all the people said they only drink beer, and there was no one that said they only drink beer and wine. If two people each said they drink either all three types of beverage or only liquor and the rest of the people drink only beer and liquor, how many people said they drink don't drink wine?

A. 34
B. 28
C. 23
D. 20
E. 11

The portion in red does not convey a clear meaning.
I believe that it is intended to convey the following:
Two people said that they drink all three types of liquor, while another two people said that they drink only liquor.

Total = (Only W) + (Only L) + (Only B) + (Only W and L) + (Only W and B) + (Only L and B) + (all 3).

Given values:
Total = 44.
Only W = 10.
Only W and L = 4.
Only B = (1/4)(44) = 11.
Only B and W = 0.
All 3 = 2.
Only L = 2.

Plugging these values into the blue equation, we get:
44 = 10 + 2 + 11 + 4 + 0 + (Only L and B) + 2
44 = 29 + (Only L and B)
(Only L and B) = 15.

Thus:
Total non-wine drinkers = (Only L) + (Only B) + (Only L and B) = 2 + 11 + 15 = 28.

The correct answer is B.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 am; Location: New York, NY; Thanked: 39 times; Followed by:22 members

by Jeff@TargetTestPrep » Wed Dec 13, 2017 10:04 am

Mo2men wrote:A marketing company doing a survey at a local nightspot asked 44 drinkers about their alcohol preferences. 10 people said they drink only wine, while 4 people said they only drink wine and hard liquor. One-fourth of all the people said they only drink beer, and there was no one that said they only drink beer and wine. If two people each said they drink either all three types of beverage or only liquor and the rest of the people drink only beer and liquor, how many people said they drink don't drink wine?

A. 34
B. 28
C. 23
D. 20
E. 11

To solve this problem, we need to determine the number of people who drink wine because 44 - the number of people who drink wine = the number of people who do not drink wine.

The number of people who drink wine consists of the following four subgroups:

1) People who drink wine only
2) People who drink both wine and beer (but not liquor)
3) People who drink both wine and liquor (but not beer)
4) People who drink all three types of beverages

According to the information given in the problem, we have 10, 0, 4, and 2 in each of the subgroups, respectively. Thus the number of people who don't drink wine is:

44 - (10 + 0 + 4 + 2) = 44 - 16 = 28

Answer: B

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