M03 Q7

Question

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

PrashantPonde · Answer

Overlapping sets.jpg 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

Bunuel · Answer

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

vinnik · Answer

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

M03 Q7

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards