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# Foodmart customers regularly buy at least one of the

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Foodmart customers regularly buy at least one of the [#permalink]

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23 Dec 2010, 17:33
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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%
[Reveal] Spoiler: OA
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Re: difficult overlapping sets problem [#permalink]

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23 Dec 2010, 17:39
rtaha2412 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%

100%={customers who buy milk}+{customers who buy chicken}+{customers who buy apples} - {customer who buy exactly 2 products} - 2*{customers who by exactly 3 products}+{customers who buy neither of the products}

$$100=60+50+35-x-2*10+0$$ --> $$x=25$$.

Answer: D.

For more about the formulas for 3 overlapping sets please see my post at: formulae-for-3-overlapping-sets-69014.html?hilit=rather%20memorize

Also discussed here: m03-74439.html?hilit=chicken%20milk#p786229

Hope it helps.
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Kudos [?]: 59 [0], given: 9

Re: difficult overlapping sets problem [#permalink]

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23 Dec 2010, 17:41
thanks alot i will check out that extra post
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Re: difficult overlapping sets problem [#permalink]

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23 Dec 2010, 22:51
@rtaha... the bunuel's approach of addressing this problem with formula is invincible, and is the best approach.

I was facing a lot of problems in set thory, i improved a lot by solving every problem 1) by formula of bunuel and 2) actual ven diagram
By solving this problems with ven diagram, you would basically learn why this formula is applied.
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Re: difficult overlapping sets problem [#permalink]

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25 Dec 2010, 19:59
Bunuel wrote:
rtaha2412 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%

100%={customers who buy milk}+{customers who buy chicken}+{customers who buy apples} - {customer who buy exactly 2 products} - 2*{customers who by exactly 3 products}+{customers who buy neither of the products}

$$100=60+50+35-x-2*10+0$$ --> $$x=25$$.

Answer: D.

For more about the formulas for 3 overlapping sets please see my post at: formulae-for-3-overlapping-sets-69014.html?hilit=rather%20memorize

Also discussed here: m03-74439.html?hilit=chicken%20milk#p786229

Hope it helps.

I have seen these 2 formulaes being used. What is the difference between them
P (A u B u C) = P (A) + P (B) + P (C) - [ P (A n B) + P (A n C) + P (B n C) ] + P (A n B n C)
and P (A u B u C) = P (A) + P (B) + P (C) - [ P (A n B) + P (A n C) + P (B n C) ] - 2(P (A n B n C))
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Joined: 02 Sep 2009
Posts: 34449
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Kudos [?]: 79588 [1] , given: 10022

Re: difficult overlapping sets problem [#permalink]

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26 Dec 2010, 00:41
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Expert's post
mailnavin1 wrote:
Bunuel wrote:
rtaha2412 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%

100%={customers who buy milk}+{customers who buy chicken}+{customers who buy apples} - {customer who buy exactly 2 products} - 2*{customers who by exactly 3 products}+{customers who buy neither of the products}

$$100=60+50+35-x-2*10+0$$ --> $$x=25$$.

Answer: D.

For more about the formulas for 3 overlapping sets please see my post at: formulae-for-3-overlapping-sets-69014.html?hilit=rather%20memorize

Also discussed here: m03-74439.html?hilit=chicken%20milk#p786229

Hope it helps.

I have seen these 2 formulaes being used. What is the difference between them
P (A u B u C) = P (A) + P (B) + P (C) - [ P (A n B) + P (A n C) + P (B n C) ] + P (A n B n C)
and P (A u B u C) = P (A) + P (B) + P (C) - [ P (A n B) + P (A n C) + P (B n C) ] - 2(P (A n B n C))

My post at the link I provided above (formulae-for-3-overlapping-sets-69014.html#p729340) is exactly about this issue.
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Re: difficult overlapping sets problem [#permalink]

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26 Dec 2010, 01:21
Oops sorry, missed that one. Got it now thanks a ton
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Re: Foodmart customers regularly buy at least one of the [#permalink]

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19 Dec 2015, 04:56
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Foodmart customers regularly buy at least one of the   [#permalink] 19 Dec 2015, 04:56
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# Foodmart customers regularly buy at least one of the

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