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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 above products?

Let \(b_i\) denote the percentage of buyers who regularly buy \(i\) products, and \(b_x\) the percentage of buyers who regularly purchase product \(x\) . We can construct these equations: \(\left{ \begin{eqnarray*} b_1 + 2b_2 + 3b_3 &=& b_m+b_c+b_a = 60\% + 50\% + 35\% = 145\%\\ b_1+b_2+b_3 &=& 100\%\\ b_3 &=& 10\%\\ \end{eqnarray*}\)

Subtract the second one from the first one: \(\begin{eqnarray*} b_2+2b_3 = 45\%\\ b_2 = 25\%\\ \end{eqnarray*}\)

Alternative explanation:

We can construct the equation: \(\begin{eqnarray*} 100% = (60% + 50% + 35%) - x - 2*10%\\ \end{eqnarray*}\)

In the sum (60%+50%+35%) we count customers that buy two products twice, so we have to extract \(x\) . In the same sum (60%+50%+35%) we count customers that buy three products thrice, so we have to extract 2*10%. Therefore, all customers are counted only once. The correct answer is D.

In the alternative explanation it is stated that customers that buy two products are counted twice, but aren't they counted three times? I don't quite understand.

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 above products?

(C) 2008 GMAT Club - m03#7

* 5% * 10% * 15% * 25% * 30%

Let \(b_i\) denote the percentage of buyers who regularly buy \(i\) products, and \(b_x\) the percentage of buyers who regularly purchase product \(x\) . We can construct these equations: \(\left{ \begin{eqnarray*} b_1 + 2b_2 + 3b_3 &=& b_m+b_c+b_a = 60\% + 50\% + 35\% = 145\%\\ b_1+b_2+b_3 &=& 100\%\\ b_3 &=& 10\%\\ \end{eqnarray*}\)

Subtract the second one from the first one: \(\begin{eqnarray*} b_2+2b_3 = 45\%\\ b_2 = 25\%\\ \end{eqnarray*}\)

Alternative explanation:

We can construct the equation: \(\begin{eqnarray*} 100% = (60% + 50% + 35%) - x - 2*10%\\ \end{eqnarray*}\)

In the sum (60%+50%+35%) we count customers that buy two products twice, so we have to extract \(x\) . In the same sum (60%+50%+35%) we count customers that buy three products thrice, so we have to extract 2*10%. Therefore, all customers are counted only once. The correct answer is D.

In the alternative explanation it is stated that customers that buy two products are counted twice, but aren't they counted three times? I don't quite understand.

They are counted thrice but should be counted only once. Therefore, they are deducted twice. So now they are counted once.

I could use some help on this one. I have been wracking my brain and I can't seem to understand where the T*(3-1) comes from. I understand how to handle questions with 2 groups, but I haven't been able to figure out the 3 group ones.

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 above products?

In the alternative explanation it is stated that customers that buy two products are counted twice, but aren't they counted three times? I don't quite understand.

They are actually counted thrice, this is why only 2 times it is subtracted. Because we want to keep the amount of all 3 inclusive once only.
_________________

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 above products?

Let \(b_i\) denote the percentage of buyers who regularly buy \(i\) products, and \(b_x\) the percentage of buyers who regularly purchase product \(x\) . We can construct these equations: \(\left{ \begin{eqnarray*} b_1 + 2b_2 + 3b_3 &=& b_m+b_c+b_a = 60\% + 50\% + 35\% = 145\%\\ b_1+b_2+b_3 &=& 100\%\\ b_3 &=& 10\%\\ \end{eqnarray*}\)

Subtract the second one from the first one: \(\begin{eqnarray*} b_2+2b_3 = 45\%\\ b_2 = 25\%\\ \end{eqnarray*}\)

Alternative explanation:

We can construct the equation: \(\begin{eqnarray*} 100% = (60% + 50% + 35%) - x - 2*10%\\ \end{eqnarray*}\)

In the sum (60%+50%+35%) we count customers that buy two products twice, so we have to extract \(x\) . In the same sum (60%+50%+35%) we count customers that buy three products thrice, so we have to extract 2*10%. Therefore, all customers are counted only once. The correct answer is D.

In the alternative explanation it is stated that customers that buy two products are counted twice, but aren't they counted three times? I don't quite understand.

x - sum of AnB,BnC,CnA 100 = 60% + 50% + 35% - x + 10 x=55 exactly two products = 55-3(10) = 25 hence D.

100 = M+C+A+N-T-2C N=those who bought none of the products- since the customers buy at least one of the products, N = 0 C = those who bought all three products - 10 T = those who bought exactly two of the products?

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 above products?

(A) 5% (B) 10% (C) 15% (D) 25% (E) 30%

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}

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 above products?

(A) 5% (B) 10% (C) 15% (D) 25% (E) 30%

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}

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

Why does the normal vent dig formula n(AuBuC) = n(A)+n(B)+n(C) -n(AnB) -n(AnC)-n(BnC) +n(AnBnC) Doesn't hold good here. We need to find [n(AnB)+n(AnC)+n(BnC)] We can straight away find it is 100=60+50+35-x+10 X=55 Here x represents the no. in exactly 2 sets & n(AnBnC) is counted 1 times