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This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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?

Yeah AUBUC = A + B+C - (A n B + B n C + C n A) + A n B n C

yields an answer of 55%

Not sure why using this formula is incorrect ...

Can anyone explain ?
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_______________________________________________________________________________ My GMAT Story: http://gmatclub.com/forum/750-q-50-v42-thank-you-gmat-club-82610.html

Thanks for the response. 55 is the answer I got, but that is not one of the options listed and the correct answer is 25 ... not sure how ...
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_______________________________________________________________________________ My GMAT Story: http://gmatclub.com/forum/750-q-50-v42-thank-you-gmat-club-82610.html

this is a challenge question and the answer is 25
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_______________________________________________________________________________ My GMAT Story: http://gmatclub.com/forum/750-q-50-v42-thank-you-gmat-club-82610.html

Even I got an answer of 25%. What is the OA? Draw the venn diagram and represent each shaded region with digits.

could you explain how you got 25 ? ... that would be very helpful
_________________

_______________________________________________________________________________ My GMAT Story: http://gmatclub.com/forum/750-q-50-v42-thank-you-gmat-club-82610.html

I was wondering why the basic set formula didn't apply to this question. Here is the reason:

Using the formula, we found that [A U B + B U C + A U C] = 55

However, this 55 also includes the 10% of people who buy all 3 products, and this 10% is not included once, but 3 times, because it is included in each of the 3 unions.

Therefore, 55 is not the number of people who buy only 2 products. I feel lucky to have come across this problem, else would never have realized this mistake.

Therefore, we need to subtract that 10% from each of the three - AUB,... BUC and AUC

thus 55 - 10 - 10 - 10 = 25.

This is the shortest way for getting the answer. There is another method, but that is not only time consuming, one has a greater chance of making mistakes in calculation.

Often I used other approach as I don't like to remember what formula in what case has to be applied.

1) Add all our percentages: 60+50+35 = 145. Now we need exclude double counting to get 100% 2) We count 3 times customers who buy all 3 products. So, 145 - 2*10 = 125% 3) We count 2 times customers who buy 2 products and as we need to subtract 25% to get 100%, 25% is our answer.
_________________

Often I used other approach as I don't like to remember what formula in what case has to be applied.

1) Add all our percentages: 60+50+35 = 145. Now we need exclude double counting to get 100% 2) We count 3 times customers who buy all 3 products. So, 145 - 2*10 = 125% 3) We count 2 times customers who buy 2 products and as we need to subtract 25% to get 100%, 25% is our answer.

Neat.

Thanks guys for the answers.... this clarifies my doubt
_________________

_______________________________________________________________________________ My GMAT Story: http://gmatclub.com/forum/750-q-50-v42-thank-you-gmat-club-82610.html

This question is best solved by using a Venn diagram. I dont know how to attach a diagram so am attaching a document.Please open the document and then look at the solution. This approach is least confusing,standard and error free and can be used to solve the most confusing questions involving overlapping sets.

Looking at the diagram and the question the following equations can be formed.

A + B + C + D = 60 (TOTAL MILK BUYERS) .................1 G + B + C + F = 50 (TOTAL CHICKEN BUYERS)...............2 E + D + C + F = 35 (TOTAL APPLE BUYERS)...................3

Using these 3 eq. we can determine anything. We know that A + B + C + D + E + F + G = 100 Add eq. 1,2 and 3

A + B + C + D + E + F + G + 2C + (B + D + F) = 145 100 + 2C + (B + D + F) = 145 100 + 20 + (B + D + F) = 145 B + D + F = 25%

================================ For clarifications - A = Only Milk Buyers E = Only Apple Buyers G = Only Chicken Buyers B = Milk + Chicken Buyer D = Milk + Apple Buyers F = Chicken + Apple Buyers C = Milk + Apple + chicken Buyer