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?
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Lets say,
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%
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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I stand corrected:
No of persons in exactly two of the sets: P(AnB) + P(AnC) + P(BnC) – 3P(AnBnC)
No of persons in two or more of the sets: P(AnB) + P(AnC) + P(BnC) – 2P(AnBnC)
so answer should be 15%
No of persons in exactly two of the sets: P(AnB) + P(AnC) + P(BnC) – 3P(AnBnC)
No of persons in two or more of the sets: P(AnB) + P(AnC) + P(BnC) – 2P(AnBnC)
so answer should 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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