The New Marketing Journal conducted a survey of wealthy

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...

I got 65 which is not one of the answers.

I believe the formula is
Total = A + B + C - (A&B) - (B&C) - (A&C) - 2(A&B&C)
Total = 45 + 38 + 27 - 15 - 12 - 8 - 2(5)
Total = 65

What am I doing wrong?

A&B.. etc. in the formula is for A&B only...

i think the first post answer is correct

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)

= 48 + 38+ 27 - (15 + 12 + 8) + 5
= 80

I'm getting 65 with this diagram...

6=38-15-12-5
2=27-12-8-5
17=45-8-5-15

17+8+5+15+2+12+6=65

What is wrong with it?

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.

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 ?

Universe = B+M+P-BM-MP-BP+BMP=45+38+27-15-12-8+8=80

Answer is (c)

C

start from the end of the q and work up...

all 3 - 5
B+M = 15-5
M+P = 12-5
B+P = 8-5
B = 45-10-5-3 = 27
M = 38-10-5-7 = 16
P = 27-3-5-7 = 12

5 + 10 + 7 + 3 + 27 + 16 + 12 = 80

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.

BMW=45-10-5-3=27
Mercedes=38-10-5-7=16
Porsche=12-7-5-3=12

27+16+12+10+3+7+5=80

Alternatively, we can use a formula.

45+38+27-15-8-7+5=80

Another way to look at it is to to subtract the overlap from the overlapping sets:

45+38+27 - (15+8+12-5) = 80

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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

P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + P(AnBnC)

this is the correct formula

the formula to be used is P(AuBuC) = P(A) + P(B) + P(C) – P(AnB) – P(AnC) – P(BnC) + P(AnBnC). Thanx

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

Hope it helps.

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.

16+10+5+7+12+3+27 = 80

Use Venn Diagram

Venn Diagram is very helpful, and I performed some long calculattions to illustrate the point :

45 owned BMW cars

38 owned Mercedes cars

27 owned Porsche cars

15 owned both BMW and Mercedes cars

12 owned both Mercedes and Porsche cars


8 owned both BMW and Porsche cars

5 persons owned all three types of cars


BMW OWners = Only owned BMW cars + owned both BMW and Mercedes cars + owned both BMW and Porsche cars - owned all three types of cars

Mercedes Owners = Only owned Mercedes cars + owned both BMW and Mercedes cars + owned both Mercedes and Porsche cars - owned all three types of cars

Porsche Owners = Only owned Porsche cars + owned both BMW and Porsche cars + owned both Mercedes and Porsche cars - owned all three types of cars

45 = Only owned BMW cars + 15 + 8 - 5 = > Only owned BMW cars = 45 - 18 = 27

38 = Only owned Mercedes cars + 15 + 12 - 5 => Only owned Mercedes cars = 38 - 22 = 16

27 = Only owned Porsche cars + 8 + 12 - 5 => Only owned Porsche cars = 27 - 15 = 12


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

=> Total = 27 + 16 + 12 + (15 - 5) + (12 - 5) + (8 - 5) + 5

= 43 + 12 + 10 + 7 + 3 + 5

= 43 + 22 + 15

= 80

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.