Official Solution: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%

Even though this is not a typical 2-group problem with overlapping members, we can still apply the group formula: \(Total = G_1 + G_2 + N - B\), where \(G_1, G_2\) 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: \(Total = G_1 + G_2 + G_3 + N - B - T * (3 - 1)\), where \(T\) is members of three groups and \(B\) is members of only two groups.

\(100\% = 60\% + 50\% + 35\% - B - 2 * 10\%\)

\(100\% = 145\% - B - 20\%\)

\(100\% = 125\% - B\)

\(B = 25\%\)

There is no neither group because all customers purchase at least one product.

Alternative Explanation: Assume there are 100 individual buyers. Let \(C_i\) represent the customers who regularly buy 1, 2, or 3 products, where \(i\) is the number of products. Multiply \(C_2\) by 2 and \(C_3\) by 3 to accurately represent the number of times these buyers were counted since they have purchased chicken and apples or milk, chicken, and apples but in reality are an individual buyer counted multiple times. Construct the following equations:

~~\(C_1 + 2 * C_2 + 3 * C_3 = M + C + A =\)~~

\(= 60\% + 50\% + 35\% =\)

\(= 145\%\)

\(C_1 + C_2 + C_3 = 100\%\)

\(C_3 = 10\%\) Subtract the second equation from the first one:

\(C_2 + 2 * C_3 = 45\%\)

\(C_2 + 2 * 10\% = 45\%\)

\(C_2 = 25\%\)

Alternative Explanation 2: Apply the formula for 3 overlapping sets:

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} \(100=60+50+35-x-2*10+0\) --> \(x=25\).

Answer: D

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