• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

difficult problem?

This topic has expert replies
Junior | Next Rank: 30 Posts
Posts: 13
Joined: 05 Jun 2007

difficult problem?

by dzelkas » Sun May 25, 2008 2:44 pm
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%

Legendary Member
Posts: 631
Joined: 18 Feb 2008
Thanked: 29 times
Followed by:3 members

by netigen » Sun May 25, 2008 3:56 pm
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%

Senior | Next Rank: 100 Posts
Posts: 84
Joined: 05 Feb 2008
Thanked: 8 times

by luvaduva » Sun May 25, 2008 5:05 pm
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%
3. No of persons in exactly two of the sets: P(AnB) + P(AnC) + P(BnC) – 3P(AnBnC)

Should it be 15?

Legendary Member
Posts: 631
Joined: 18 Feb 2008
Thanked: 29 times
Followed by:3 members

by netigen » Sun May 25, 2008 6:40 pm
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%

Senior | Next Rank: 100 Posts
Posts: 51
Joined: 23 Mar 2008
Location: San Francisco
Thanked: 2 times

by sukrant26 » Sun May 25, 2008 8:14 pm
60+50+35-100+10 = 55

Hence 55-3X10 = 25

Am I correct?

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3225
Joined: 08 Jan 2008
Location: Toronto
Thanked: 1710 times
Followed by:613 members
GMAT Score:800

Re: difficult problem?

by Stuart@KaplanGMAT » Sun May 25, 2008 10:13 pm
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%
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.

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.
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course