percentage

[ritula]

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?

5%
10%
15%
25%
30%

[parallel_chase]

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?

5%
10%
15%
25%
30%

x = customers who bought 2 products

Total = product 1 + product 2 + product 3 - x - 2*(all three)

100 = 60+50+35 -x - 2*10

x = 145 - 20 - 100

x = 25%

Whats the OA?

[Fab]

Why?

- 2*(all three)

specially, why are you multiplying by 2....?

Thanks

[parallel_chase]

Here is the formula for three set overlapping

Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither

[Fab]

Thank you.

[earth@work]

formula explanation...

use venn diagram in this problem:
Let those who buy milk=m, those who buy chicken=C, who buy apples=A
Total = only M+only C+onlyA + those who buy two+ those who buy all three
let x=those who buy both M&C
y=C&A
z=M&A
only M =(60-x-z-10)
only C = (50-x-y-10)
only A = (35-z-y-10)
Total=(60-x-z-10)+(50-x-y-10)+(35-z-y-10)+(x+y+z)+10
total=60+50+35-who buy two-2*10
proved

[ritula]

Nice explanation. Made the things so simple. Thanks
yes Ans is 25%

formula explanation...

use venn diagram in this problem:
Let those who buy milk=m, those who buy chicken=C, who buy apples=A
Total = only M+only C+onlyA + those who buy two+ those who buy all three
let x=those who buy both M&C
y=C&A
z=M&A
only M =(60-x-z-10)
only C = (50-x-y-10)
only A = (35-z-y-10)
Total=(60-x-z-10)+(50-x-y-10)+(35-z-y-10)-(x+y+z)+10
total=60+50+35-who buy two-2*10
proved

[stop@800]

Just use the formula:

total = A + B + C - 2*(all3) - (only two)

The question: why multiply by 2?

We are actually subtracting overlaps from A + B + C
in A+B+C, the AB + BC + CA has been counted twice so we are subtracting it once
and
ABC has been counted thrice [one with each AB BC CA] so we are subtracting it twice.

Please draw the venn diagram, you will get absolutely clear picture.

[bhumika.k.shah]

Thanks!

I never came across this formula before...
i hope this would help me during D-day

Here is the formula for three set overlapping

Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither