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Foodmart customers regularly buy at least one of the following product [#permalink]
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02 Mar 2010, 19:45
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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% I am not convinced with the explanation given. There was also an alternative explanation, which wasn't very clear either  Even though this is not a typical 2group problem with overlapping members, we can still apply the group formula: Total = G1 + G2 + N  B, where G1, G2 are group 1 and group 2, N is neither, and B is both. Because we have more than 2 groups, we need to adjust the formula to reflect customers purchasing 3 products and therefore being members of 3 groups, and being counted as 3 distinct customers. The formula needs to be modified as follows: Total = G1 + G2 + G3 + N  B  T*(31) , where T is members of three groups and B is members of only two groups.
There is no neither group because all customers purchase at least one product. The correct answer is D.
I suspect the formula for three overlapping sets used in the question. Can someone confirm it. OPEN DISCUSSION OF THIS QUESTION IS HERE: foodmartcustomersregularlybuyatleastoneofthe106823.html
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Re: Foodmart customers regularly buy at least one of the following product [#permalink]
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02 Mar 2010, 21:36
BarneyStinson 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%
I am not convinced with the explanation given. There was also an alternative explanation, which wasn't very clear either  Even though this is not a typical 2group problem with overlapping members, we can still apply the group formula: Total = G1 + G2 + N  B, where G1, G2 are group 1 and group 2, N is neither, and B is both. Because we have more than 2 groups, we need to adjust the formula to reflect customers purchasing 3 products and therefore being members of 3 groups, and being counted as 3 distinct customers. The formula needs to be modified as follows: Total = G1 + G2 + G3 + N  B  T*(31) , where T is members of three groups and B is members of only two groups.
There is no neither group because all customers purchase at least one product. The correct answer is D.
I suspect the formula for three overlapping sets used in the question. Can someone confirm it. The formula is n(AUBUC) = n(A)+n(B)+n(C)B+AN where B is both (it will sum of (A&B), (B&C), (C&A)). and A is All and N is neither so plugging in we get 100 = 60+50+35+10B0 B = 55. exactly two = 55  3(10) = 25 subtracting 10% three times as this value is including in all the (A&B), (B&C), (C&A).



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Re: Foodmart customers regularly buy at least one of the following product [#permalink]
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04 Mar 2010, 22:01
bangalorian2000 wrote: The formula is n(AUBUC) = n(A)+n(B)+n(C)B+AN where B is both (it will sum of (A&B), (B&C), (C&A)). and A is All and N is neither so plugging in we get 100 = 60+50+35+10B0 B = 55. exactly two = 55  3(10) = 25 subtracting 10% three times as this value is including in all the (A&B), (B&C), (C&A). Gotcha bro!!! You are indeed smart!!!
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Re: Foodmart customers regularly buy at least one of the following product [#permalink]
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15 Nov 2014, 00:40
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Re: Foodmart customers regularly buy at least one of the following product [#permalink]
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15 Nov 2014, 04:58
BarneyStinson 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% I am not convinced with the explanation given. There was also an alternative explanation, which wasn't very clear either  Even though this is not a typical 2group problem with overlapping members, we can still apply the group formula: Total = G1 + G2 + N  B, where G1, G2 are group 1 and group 2, N is neither, and B is both. Because we have more than 2 groups, we need to adjust the formula to reflect customers purchasing 3 products and therefore being members of 3 groups, and being counted as 3 distinct customers. The formula needs to be modified as follows: Total = G1 + G2 + G3 + N  B  T*(31) , where T is members of three groups and B is members of only two groups.
There is no neither group because all customers purchase at least one product. The correct answer is D.
I suspect the formula for three overlapping sets used in the question. Can someone confirm it. 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}\(100=60+50+35x2*10+0\) > \(x=25\). Answer: D. OPEN DISCUSSION OF THIS QUESTION IS HERE: foodmartcustomersregularlybuyatleastoneofthe106823.html
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