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Sets Problem

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Sets Problem [#permalink] New post 11 Jan 2010, 09:38
Hi Experts,

Can anybody help me in the below question?

Q: 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%

Thanks in advance.
-Amit
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Re: Sets Problem [#permalink] New post 11 Jan 2010, 11:13
amitanand wrote:
Hi Experts,

Can anybody help me in the below question?

Q: 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%

Thanks in advance.
-Amit


60 buy milk, 50 buy chicken, 35 buy apples out of a total of 100
10 buy all three products so 50 buy milk, 40 buy chicken, 25 buy apples
50 + 40 + 25 + 10 = 125
answer d = 25
25 buy milk 15 buy chicken 25 buy apples 10 buy all three and 25 buy two
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Re: Sets Problem [#permalink] New post 11 Jan 2010, 11:46
Thank you very much.
-Amit
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Re: Sets Problem [#permalink] New post 11 Jan 2010, 12:05
60 buy milk, 50 buy chicken, 35 buy apples out of a total of 100
10 buy all three products so 50 buy milk, 40 buy chicken, 25 buy apples
50 + 40 + 25 + 10 = 125
answer d = 25
25 buy milk 15 buy chicken 25 buy apples 10 buy all three and 25 buy two


Just one quick one:
-------------------
1. Why we are not subtracting 25 from apples in the last sentence.
2. Is it possible to explain in more detail like by mentioning (for milk 60-10=50, that includes only Milk,Milk-Chicken, Milk-Apples) etc...
The reason being, I am still not getting the complete grip on the concept behind this question.
Many thanks in anticipation.
-Amit
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Re: Sets Problem [#permalink] New post 11 Jan 2010, 13:06
amitanand wrote:
60 buy milk, 50 buy chicken, 35 buy apples out of a total of 100
10 buy all three products so 50 buy milk, 40 buy chicken, 25 buy apples
50 + 40 + 25 + 10 = 125
answer d = 25
25 buy milk 15 buy chicken 25 buy apples 10 buy all three and 25 buy two


Just one quick one:
-------------------
1. Why we are not subtracting 25 from apples in the last sentence.
2. Is it possible to explain in more detail like by mentioning (for milk 60-10=50, that includes only Milk,Milk-Chicken, Milk-Apples) etc...
The reason being, I am still not getting the complete grip on the concept behind this question.
Many thanks in anticipation.
-Amit


Yes, you could have subtracted from 25 apples and arrived at the same answer. Are you familiar with Venn Diagrams? I don't have the tools to create one, but that is the easiest approach. Hopefully someone will come on here and create a diagram for you.

If there are three circles in the Venn Diagram then there are 7 areas to be counted: Milk only, chicken only, and apples only. The other four areas are comprised of overlapping areas (hence the name overlapping sets). one area is the overlap of milk-chicken, milk-apples, and chicken-apples and the fourth area is the overlap of all three.

If you insert any number in the double overlap or the triple overlap then you must subtract that number from milk, chicken and/or apples.

60 only, 50 only, and 35 only is what you have and 10 with all three overlap
that gives you 50 only milk, 40 only chicken, 25 only apples, and 10 all three = 125

The answer we are looking for is one of the three areas where there is only a double overlap. Now, you can break out the 25 into all three areas, two areas, or one area. Unless we are asked a specific area, for example, the number of both chicken and milk or chicken and apples, then just pick one to make things easy on yourself.

In this case I just picked chicken and milk at 25

So now we have 25 only milk, 15 only chicken, 25 only apples, 10 all three, 25 milk-chicken, 0 milk-apples, and 0 chicken-apples.

We could have easily said 15 milk and chicken and 10 milk and apples
That would have given us 25 Milk, 25 chicken, 15 apples, 10 all three, 15 milk-chicken, 10 milk-apples, 0 chicken-apples

The reason milk is 25 is because 60 -10 - 15-10
The reason chicken is 25 is because 50-10-15
The reason 15 apples is because 35-10-10
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Re: Sets Problem [#permalink] New post 11 Jan 2010, 13:20
Apply the Union of three sets formula. The answer should be 15% which is option C.
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Re: Sets Problem   [#permalink] 11 Jan 2010, 13:20
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