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# Foodmart customers regularly buy at least one of the followi

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Manager
Joined: 09 Feb 2010
Posts: 70
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02 Sep 2010, 08:47
00:00

Difficulty:

25% (medium)

Question Stats:

83% (01:37) correct 17% (01:22) wrong based on 36 sessions

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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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Joined: 02 Sep 2009
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Kudos [?]: 79324 [0], given: 10016

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02 Sep 2010, 09:19
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}

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

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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02 Sep 2010, 09:26
1
KUDOS
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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02 Sep 2010, 09:27
Kudos to you guyz...
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Last edited by fatihaysu on 03 Sep 2010, 03:13, edited 1 time in total.
Manager
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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)
Re: Venn diagram question   [#permalink] 03 Sep 2010, 11:07
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