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foodmart customers

by rahul.s » Sat Jan 30, 2010 5:05 am
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%

OA: D
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by sars72 » Sat Jan 30, 2010 5:30 am
Forming the following venn diagram,
Image


60+50+35 - [(x+y) +(y+z) + (x+z)] + 10 = 100

-> 145 + 10 - (2x+2y+2z) = 100

155-100 = 2(x+y+z)

-> 55/2 = x+y+z = 27.5

Getting a decimal point answer :( . Please help!
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by ajith » Sat Jan 30, 2010 5:49 am
sars72 wrote:Forming the following venn diagram,
Image


60+50+35 - [(x+y) +(y+z) + (x+z)] + 10 = 100

-> 145 + 10 - (2x+2y+2z) = 100

155-100 = 2(x+y+z)

-> 55/2 = x+y+z = 27.5

Getting a decimal point answer :( . Please help!
As far I see it the solution is correct. Do not be bothered about getting fractional answer since it is a percentage and not an absolute number
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by sanju09 » Sat Jan 30, 2010 5:53 am
rahul.s wrote: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%

OA: D
Take n (M ∪ C ∪ A) = 100 so that n (M ∩ C ∩ A) = 10.

Now, note:

n (M ∪ C ∪ A) = n (M) + n (C) + n (A) - n (M ∩ C) - n (C ∩ A) - n (M ∩ A) + n (M ∩ C ∩ A)

I know, it is more than GMAT, but, ok...

n (M ∩ C) + n (C ∩ A) + n (M ∩ A) = n (M) + n (C) + n (A) - n (M ∪ C ∪ A) + n (M ∩ C ∩ A) = 60 + 50 + 35 - 100 + 10 = 55.

Take n (M ∩ C ∩ A) = 10, out 3 times of it, to answer what is asked; 55 - 3*10 = [spoiler]25[/spoiler].

[spoiler]D[/spoiler]
Last edited by sanju09 on Sat Jan 30, 2010 5:57 am, edited 2 times in total.
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by rahul.s » Sat Jan 30, 2010 5:55 am
27.5 is between 25 and 30. so it could be D or E
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by bhumika.k.shah » Sat Jan 30, 2010 5:55 am
r u sure this is the end to the sum?
sars72 wrote:Forming the following venn diagram,
Image


60+50+35 - [(x+y) +(y+z) + (x+z)] + 10 = 100

-> 145 + 10 - (2x+2y+2z) = 100

155-100 = 2(x+y+z)

-> 55/2 = x+y+z = 27.5

Getting a decimal point answer :( . Please help!
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by rahul.s » Sat Jan 30, 2010 6:34 am
sorry folks. this one's already been solved. follow the link

https://www.beatthegmat.com/percentage-t19027.html

cheers!
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by ajith » Sat Jan 30, 2010 6:44 am
Image

60-x-y-10 + 50-x-z-10 +35-y-z + x+y+z +10 = 100 [initial solution posted has a problem with this part]

[Yellow areas + Green areas + Red area - refer the picure]

125 - x -y -z = 100

x+y+z = 25

hence 25
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by sanju09 » Sat Jan 30, 2010 6:47 am
rahul.s wrote:sorry folks. this one's already been solved. follow the link

https://www.beatthegmat.com/percentage-t19027.html

cheers!
Ultimately, I made you people use

n (M ∩ C) + n (C ∩ A) + n (M ∩ A) = n (M) + n (C) + n (A) - n (M ∪ C ∪ A) + n (M ∩ C ∩ A) - 3* n (M ∩ C ∩ A)

This is same as

x = customers who bought 2 products = product 1 + product 2 + product 3 - Total + (all three) - 3*(all three)

Or x = customers who bought 2 products = product 1 + product 2 + product 3 - Total - 2*(all three)
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