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The New Marketing Journal conducted a survey of wealthy [#permalink]
14 Aug 2010, 12:59

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55% (hard)

Question Stats:

61% (02:49) correct
39% (01:52) wrong based on 172 sessions

The New Marketing Journal conducted a survey of wealthy German car owners. According to the survey, all wealthy car owners owned one or more of the following three brands: BMW, Mercedes, or Porsche. Respondents' answers were grouped as follows: 45 owned BMW cars 38 owned Mercedes cars, and 27 owned Porsche cars. Of these, 15 owned both BMW and Mercedes cars, 12 owned both Mercedes and Porsche cars, 8 owned both BMW and Porsche cars, and 5 persons owned all three types of cars. How many different individuals were surveyed?

Re: Overlapping Sets [#permalink]
12 Dec 2010, 19:17

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This post received KUDOS

Expert's post

zmaster85 wrote:

The New Marketing Journal conducted a survey of wealthy German car owners. According to the survey, all wealthy car owners owned one or more of the following three brands: BMW, Mercedes, or Porsche. Respondents' answers were grouped as follows: 45 owned BMW cars 38 owned Mercedes cars, and 27 owned Porsche cars. Of these, 15 owned both BMW and Mercedes cars, 12 owned both Mercedes and Porsche cars, 8 owned both BMW and Porsche cars, and 5 persons owned all three types of cars. How many different individuals were surveyed?

A) 70 B) 75 C) 80 D) 110 E) 130

It is a straight forward question that can be solved using the formula discussed above but if you forget it, you can use a Venn diagram. Start with the region where all 3 sets overlap. That is 5. Next work on each of the three regions where 2 sets overlap. Next work on the 3 regions where people own a single car. Add the number of people in all the regions and you get the total number of people.

Re: Overlapping Sets [#permalink]
12 Oct 2010, 02:36

1

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Expert's post

prab wrote:

i believe formula should be : P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + 2 P(AnBnC), using this the ans would be 65, but 65 is no where in the option, but using P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + P(AnBnC) we get 80. which is one of the options(ans seems to be the correct option). which formula is correct. Any one? i cant figure out what am i doing wrong here

Re: Overlapping Sets [#permalink]
14 Aug 2010, 13:10

zmaster85 wrote:

The New Marketing Journal conducted a survey of wealthy German car owners. According to the survey, all wealthy car owners owned one or more of the following three brands: BMW, Mercedes, or Porsche. Respondents' answers were grouped as follows: 45 owned BMW cars 38 owned Mercedes cars, and 27 owned Porsche cars. Of these, 15 owned both BMW and Mercedes cars, 12 owned both Mercedes and Porsche cars, 8 owned both BMW and Porsche cars, and 5 persons owned all three types of cars. How many different individuals were surveyed?

A) 70 B) 75 C) 80 D) 110 E) 130

P(A u B u C) : P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) + P(A n B n C)

Re: Overlapping Sets [#permalink]
14 Aug 2010, 15:44

vasili wrote:

Not sure if wording of my reply is correct.

Total= Set1+Set2-Both+Neither( in our case it's 0)

X=45+38+27-(8+15+12+5)=70

I think your formula (Bunuel has this in one of his other posts) is for the case when "Both" applies to the population such that they only own those 2 cars, that does not seem to be the case here. So we shoudl go with the usual formula above and get 80. I don't see 70. X = A+B+C-(only2)-2AandBandC - I think this is the formula you were attempting... _________________

Re: Overlapping Sets [#permalink]
19 Aug 2010, 12:33

I agree with swdatta and Financier but I don't understand why it's wrong... You should deduct the people who own all three types of cars twice otherwise you would count them several times. _________________

Re: Overlapping Sets [#permalink]
07 Oct 2010, 11:28

zmaster85 wrote:

The New Marketing Journal conducted a survey of wealthy German car owners. According to the survey, all wealthy car owners owned one or more of the following three brands: BMW, Mercedes, or Porsche. Respondents' answers were grouped as follows: 45 owned BMW cars 38 owned Mercedes cars, and 27 owned Porsche cars. Of these, 15 owned both BMW and Mercedes cars, 12 owned both Mercedes and Porsche cars, 8 owned both BMW and Porsche cars, and 5 persons owned all three types of cars. How many different individuals were surveyed?

A) 70 B) 75 C) 80 D) 110 E) 130

Let the set of owners be B,M,P B=45 M=38 P=27 \(B \cap M=15\) \(P \cap M=12\) \(B \cap P=8\) \(B \cap M \cap P=5\) Q : How many were questioned ? Or in other words size of the universe ?

Re: Overlapping Sets [#permalink]
11 Oct 2010, 06:52

To help clarify some of the confusion:

Conisder a situation where there are only two things in an overlapping set (X and Y). There are 20 people in X; 15 people in Y; 5 people in X and Y. In this case, the size of the population would be x+y-xy = 20+15-5 = 30.

Apply this same principle to the overlapping sets of the three cars:

15 people own BMW and Mercedes. 5 people own a BMW, Mercedes and Porsche. However, these two data points are counting owners of BMW and Mercedes twice. The same applies for the 12 owners of a Mercedes and Porsche and the 8 owners of BMW and Porsche.

If you solved this using a Venn Diagram, you must first account for the overlap in the overlapping sets.

15-5=10 12-5=7 08-5=3

At this point you can find the number of unique drivers of each model.

Re: Overlapping Sets [#permalink]
12 Oct 2010, 01:54

i believe formula should be : P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + 2 P(AnBnC), using this the ans would be 65, but 65 is no where in the option, but using P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + P(AnBnC) we get 80. which is one of the options(ans seems to be the correct option). which formula is correct. Any one? i cant figure out what am i doing wrong here

Re: Overlapping Sets [#permalink]
12 Oct 2010, 01:56

prab wrote:

i believe formula should be : P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + 2 P(AnBnC), using this the ans would be 65, but 65 is no where in the option, but using P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + P(AnBnC) we get 80. which is one of the options(ans seems to be the correct option). which formula is correct. Any one? i cant figure out what am i doing wrong here

Total = Only owned BMW cars + Only owned Mercedes cars + Only owned Porsche cars + Only owned both BMW and Mercedes cars + Only owned both Mercedes and Porsche cars + ONly owned both BMW and Porsche cars + owned all three types of cars

Two formulas of 3 overlapping sets: formulae-for-3-overlapping-sets-69014.html#p729340

Bunuel's link explains it all.

I too did the Venn Diagram and came up with 65. However, I overlooked a fact; with 3 groups, the intersection of 2 groups includes the intersection of 3 groups. So everytime you subtract MnB, MnP, BnP, you also subtract MnBnP. In the end, you subtract MnBnP one too many times, therefore, must add it back in once.

Back to hometown after a short trip to New Delhi for my visa appointment. Whoever tells you that the toughest part gets over once you get an admit is...