I can't seem to figure out the below problem. Can someone please help

the correct answer should be 25%

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 2 of the above products?

a) 5%

b) 10%

c) 15%

d) 25%

e) 30%

## difficult problem?

##### This topic has expert replies

Milk = M

Chicken = C

Apple = A

MAC = intersection of Milk, chicken and apple

similarly,

MA = intersection of Milk and apple

MC = intersection of Milk, chicken

AC = intersection of chicken and apple

then

100 = M + A + C - (MA+MC+AC) + MAC

(MA+MC+AC) = 60+50+35-100+10 = 45

We need to find all cases where only 2 items are purchased = (MA+MC+AC) - 2 x MAC = 45 - 2 x 10 = 25%

3. No of persons in exactly two of the sets: P(AnB) + P(AnC) + P(BnC) – 3P(AnBnC)netigen wrote:Lets say,

We need to find all cases where only 2 items are purchased = (MA+MC+AC) - 2 x MAC = 45 - 2 x 10 = 25%

Should it be 15?

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Basically, if someone is in two groups they're counted twice, so we need to subtract them once; if someone is counted in three groups they're counted three times, so we need to subtract them twice.dzelkas wrote:I can't seem to figure out the below problem. Can someone please help

the correct answer should be 25%

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 2 of the above products?

a) 5%

b) 10%

c) 15%

d) 25%

e) 30%

So:

True # = total group a + total group b + total group c - (ab + ac + bc) - 2(abc)

100 = 60 + 50 + 35 - (doubles) - 2(triples)

100 = 145 - 2(10) - doubles

doubles = 145 - 20 - 100

doubles= 145 - 120 = 25

Note that if there were also some people in none of the 3 groups, the formula would have been:

True # = total group a + total group b + total group c - (ab + ac + bc) - 2(abc) + total in none of a/b/c

but in this question we know that every shopper buys at least one product.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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