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PS: Foodmart (Milk,Chicken,Apples) (Venn&Prob Q)

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PS: Foodmart (Milk,Chicken,Apples) (Venn&Prob Q) [#permalink] New post 21 Apr 2009, 21:34
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Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?

a* 5%
b* 10%
c* 15%
d* 25%
e* 30%
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Re: PS: Foodmart (Milk,Chicken,Apples) (Venn&Prob Q) [#permalink] New post 22 Apr 2009, 18:18
( A U B U C ) = A + B + C - ( A n B + B n C + C n A ) - 2 ( A n B n C)

100 = 60 + 50 + 35 - ( x ) - 2 ( 10 )

x = 125 - 100 = 25 %

Ans . D
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Re: PS: Foodmart (Milk,Chicken,Apples) (Venn&Prob Q) [#permalink] New post 30 Apr 2009, 01:06
Can you tell me where is this formulae?

because i know only one

AUBUC = A + B+C - (A n B + B n C + C n A) + A n B n C

can you please explain?

tkarthi4u wrote:
( A U B U C ) = A + B + C - ( A n B + B n C + C n A ) - 2 ( A n B n C)

100 = 60 + 50 + 35 - ( x ) - 2 ( 10 )

x = 125 - 100 = 25 %

Ans . D
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Re: PS: Foodmart (Milk,Chicken,Apples) (Venn&Prob Q) [#permalink] New post 02 Jul 2009, 13:22
Yeah AUBUC = A + B+C - (A n B + B n C + C n A) + A n B n C

yields an answer of 55%

Not sure why using this formula is incorrect ...

Can anyone explain ?
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Re: PS: Foodmart (Milk,Chicken,Apples) (Venn&Prob Q) [#permalink] New post 02 Jul 2009, 14:45
A - milk buyers = 60%
B - chicken buyers = 50%
C - apple buyers = 35%

Now A U B U C is the total number of shoppers in the mart, who buy one or more of the goods. This has to be = 100%

A n B n C are those who buy all 3 products = 10%

A n B = buy milk and chicken, but NOT apples
B n C = buy chicken and apples, not milk
A n C = buy milk and apples, not chicken

We have to find the sum of these 3 mentioned above (ie, percentage of people buying exactly 2 things). Let this sum be X

so applying the formula mentioned above

100% = 60 + 50 + 35 - X + 10
X = 55

hope the logic is clear.
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Re: PS: Foodmart (Milk,Chicken,Apples) (Venn&Prob Q) [#permalink] New post 02 Jul 2009, 14:59
Thanks for the response. 55 is the answer I got, but that is not one of the options listed and the correct answer is 25 ... not sure how ...
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Re: PS: Foodmart (Milk,Chicken,Apples) (Venn&Prob Q) [#permalink] New post 02 Jul 2009, 20:18
depends on where you got this question from. Answer need not always be right. Let us know the source, so we can check
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Re: PS: Foodmart (Milk,Chicken,Apples) (Venn&Prob Q) [#permalink] New post 03 Jul 2009, 04:42
Even I got an answer of 25%.
What is the OA?
Draw the venn diagram and represent each shaded region with digits.
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Re: PS: Foodmart (Milk,Chicken,Apples) (Venn&Prob Q) [#permalink] New post 03 Jul 2009, 09:17
this is a challenge question and the answer is 25
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Re: PS: Foodmart (Milk,Chicken,Apples) (Venn&Prob Q) [#permalink] New post 03 Jul 2009, 09:18
shrutisingh wrote:
Even I got an answer of 25%.
What is the OA?
Draw the venn diagram and represent each shaded region with digits.



could you explain how you got 25 ? ... that would be very helpful
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Re: PS: Foodmart (Milk,Chicken,Apples) (Venn&Prob Q) [#permalink] New post 03 Jul 2009, 10:38
I was wondering why the basic set formula didn't apply to this question. Here is the reason:

Using the formula, we found that [A U B + B U C + A U C] = 55

However, this 55 also includes the 10% of people who buy all 3 products, and this 10% is not included once, but 3 times, because it is included in each of the 3 unions.

Therefore, 55 is not the number of people who buy only 2 products. I feel lucky to have come across this problem, else would never have realized this mistake.

Therefore, we need to subtract that 10% from each of the three - AUB,... BUC and AUC

thus 55 - 10 - 10 - 10 = 25.

This is the shortest way for getting the answer. There is another method, but that is not only time consuming, one has a greater chance of making mistakes in calculation.
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Re: PS: Foodmart (Milk,Chicken,Apples) (Venn&Prob Q) [#permalink] New post 03 Jul 2009, 10:47
Expert's post
Often I used other approach as I don't like to remember what formula in what case has to be applied.

1) Add all our percentages: 60+50+35 = 145.
Now we need exclude double counting to get 100%
2) We count 3 times customers who buy all 3 products. So, 145 - 2*10 = 125%
3) We count 2 times customers who buy 2 products and as we need to subtract 25% to get 100%, 25% is our answer.
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Re: PS: Foodmart (Milk,Chicken,Apples) (Venn&Prob Q) [#permalink] New post 03 Jul 2009, 15:08
walker wrote:
Often I used other approach as I don't like to remember what formula in what case has to be applied.

1) Add all our percentages: 60+50+35 = 145.
Now we need exclude double counting to get 100%
2) We count 3 times customers who buy all 3 products. So, 145 - 2*10 = 125%
3) We count 2 times customers who buy 2 products and as we need to subtract 25% to get 100%, 25% is our answer.



Neat.

Thanks guys for the answers.... this clarifies my doubt
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Re: PS: Foodmart (Milk,Chicken,Apples) (Venn&Prob Q) [#permalink] New post 03 Jul 2009, 23:44
This question is best solved by using a Venn diagram.
I dont know how to attach a diagram so am attaching a document.Please open the document and then look at the solution.
This approach is least confusing,standard and error free and can be used to solve the most confusing questions involving overlapping sets.

Looking at the diagram and the question the following equations can be formed.

A + B + C + D = 60 (TOTAL MILK BUYERS) .................1
G + B + C + F = 50 (TOTAL CHICKEN BUYERS)...............2
E + D + C + F = 35 (TOTAL APPLE BUYERS)...................3

Using these 3 eq. we can determine anything.
We know that A + B + C + D + E + F + G = 100
Add eq. 1,2 and 3

A + B + C + D + E + F + G + 2C + (B + D + F) = 145
100 + 2C + (B + D + F) = 145
100 + 20 + (B + D + F) = 145
B + D + F = 25%

================================
For clarifications -
A = Only Milk Buyers
E = Only Apple Buyers
G = Only Chicken Buyers
B = Milk + Chicken Buyer
D = Milk + Apple Buyers
F = Chicken + Apple Buyers
C = Milk + Apple + chicken Buyer
Attachments

Venn.doc [25 KiB]
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Last edited by mdfrahim on 03 Jul 2009, 23:46, edited 1 time in total.
Re: PS: Foodmart (Milk,Chicken,Apples) (Venn&Prob Q)   [#permalink] 03 Jul 2009, 23:44
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