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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 followi [#permalink]

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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%
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Re: Venn diagram question [#permalink]

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New post 02 Sep 2010, 09:19
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zest4mba wrote:
Can someone solve this using a venn diagram

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?
5%
10%
15%
25%
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

Hope it helps.
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Re: Venn diagram question [#permalink]

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New post 02 Sep 2010, 09:26
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60-(x+10+z) + 50-(x+10+y) + 35-(z+10+y) + x + +y + z +10 = 100

where x = people who bought Milk & Chicken
y = people who bought chicken & Apples
z= people who bought Milk and Apples
x+y+z= the number of people who bought just exactly two products.

Hence solving the above equation we get,

125 -(x+y+z) = 100
Thus, x+y+z= 25

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Re: Venn diagram question [#permalink]

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New post 03 Sep 2010, 11:07
Hi Bunuel

I was looking at this post

formulae-for-3-overlapping-sets-69014.html?hilit=rather%20memorize

Can you tell me the above question of milk, chicken and apples would be as per which of the below points and how

1. For 3 sets A, B, and C: 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)

2. To determine the No of persons in exactly one set : P(A) + P(B) + P(C) – 2P(A n B) – 2P(A n C) – 2P(B n C) + 3P(A n B n C)

3. To determine the No of persons in exactly two of the sets : P(A n B) + P(A n C) + P(B n C) – 3P(A n B n C)

4. To determine the No of persons in exactly three of the sets : P(A n B n C)

5. To determine the No of persons in two or more sets (at least 2 sets) : P(A n B) + P(A n C) + P(B n C) – 2P(A n B n C)

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

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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%

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Re: difficult overlapping sets problem [#permalink]

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New post 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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New post 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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Re: difficult overlapping sets problem [#permalink]

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New post 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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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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