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M03 Q7

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M03 Q7 [#permalink] New post 19 Jan 2013, 13:29
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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%

Can anyone please explain the underlined part of the following formula:-
100%={customers who buy milk}+{customers who buy chicken}+{customers who buy apples} - {customer who buy exactly 2 products} - 2*{customers who by exactly 3 products}+{customers who buy neither of the products}

Why we have multiplied 2 with {customers who by exactly 3 products} and subtracted by {customer who buy exactly 2 products} ?

Looking forward to your replies.

Thanks & Regards
Vinni
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Re: M03 Q7 [#permalink] New post 19 Jan 2013, 14:05
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Attachment:
Overlapping sets.jpg
Overlapping sets.jpg [ 38.52 KiB | Viewed 245 times ]


Your doubt: Why we have multiplied 2 with {customers who by exactly 3 products} and subtracted by {customer who buy exactly 2 products} ?
-- This is because Once you add up "{customers who buy milk}+{customers who buy chicken}+{customers who buy apples}" you are already double counting {customer who buy exactly 2 products} and triple counting {customers who by exactly 3 products}. Hence you subtract the additional ones.

Let’s analyze above based on what is provided in the problem. Assume total food mart customers as 100.
{customers who buy milk}+{customers who buy chicken}+{customers who buy apples} = 60 + 50 + 35 = 145

In our diagram, it can be represented as
(a + d + g + e) + (b + d + g + f) + (c + e + g + f) = 145
(a + b + c + d + e + f + g) + (d + e + f) + 2g = 145
From the diagram, a + b + c + d + e + f + g = 100
100 + (d + e + f) + 2g = 145
100 = 145 - (d + e + f) - 2g
i.e. 100 = (milk customers + chicken customers + apple customers) - (customers who buy exactly 2 products) - 2 * (customers who buy exactly 3 products)
-- This answers your doubt.

Now lets solve the problem further
100 = 145 - (d + e + f) - 2g
(d + e + f) + 2g = 45
We know g=10,
Hence, customers who purchase exactly 2 products = (d + e + f) = 25

Thus choice(D) is the answer
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PraPon

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Last edited by PraPon on 19 Jan 2013, 14:10, edited 1 time in total.
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Re: M03 Q7 [#permalink] New post 19 Jan 2013, 14:09
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vinnik wrote:
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%

Can anyone please explain the underlined part of the following formula:-
100%={customers who buy milk}+{customers who buy chicken}+{customers who buy apples} - {customer who buy exactly 2 products} - 2*{customers who by exactly 3 products}+{customers who buy neither of the products}

Why we have multiplied 2 with {customers who by exactly 3 products} and subtracted by {customer who buy exactly 2 products} ?

Looking forward to your replies.

Thanks & Regards
Vinni


See detailed explanation of the formula in "ADVANCED OVERLAPPING SETS" chapter of Math Book: advanced-overlapping-sets-problems-144260.html

Hope it helps.
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Manager
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Re: M03 Q7 [#permalink] New post 20 Jan 2013, 11:03
Thanks PraPon for this nice and detailed explanation. This particular concept has now become easier to understand.
And Bunuel, thanks for the link.

Appreciate your replies.

Regards
Vinni
Re: M03 Q7   [#permalink] 20 Jan 2013, 11:03
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