Foodmart customers regularly buy at least one of the

Question

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%

M03-07

A. 5% 
B. 10% 
C. 15% 
D. 25% 
E. 30%

M03-07

Bunuel · Accepted Answer

19. Overlapping Sets 
     Theory   
 Overlapping Sets Made Easy! 
 How to draw a Venn Diagram for problems 
 ADVANCED OVERLAPPING SETS PROBLEMS  
 Formulae for 3 overlapping sets 
     Questions   
 The E-GMAT Sets Triad: 3 Exciting Sets Questions! 
 The Word “Or” in GMAT Math 
 DS Questions 
 PS Questions

For more:
 ALL YOU NEED FOR QUANT ! ! ! 
 Ultimate GMAT Quantitative Megathread

Bunuel · Answer

Official Solution:

At Foodmart, customers always purchase at least one of the following items: milk, chicken, or apples. Among the shoppers, 60% buy milk, 50% buy chicken, and 35% buy apples. If 10% of the customers purchase all three products, what percentage of Foodmart customers buy exactly two of the three items ?

A. 5%
B. 10%
C. 15%
D. 25%
E. 30%

Apply the formula for three overlapping sets:
 
100% = (customers who buy milk) + (customers who buy chicken) + (customers who buy apples) - (customers who buy exactly 2 products) - 2*(customers who buy all 3 products) + (customers who buy none of the products)
 
When adding the percentages for groups A, B, and C (milk, chicken, and apples), certain sections are counted more than once. For example, customers who buy exactly 2 products are counted twice because they are included in both of the product pairs they purchase. Similarly, customers who buy all 3 products are counted three times, once for each product group. To account for this, we subtract the percentage of customers who buy exactly 2 products ONCE (to count this group only once) and the percentage of customers who buy all 3 products TWICE (to count these customers only once as well).
 
For more information and examples, check out this link:  ADVANCED OVERLAPPING SETS PROBLEMS 
 
Thus, according to the above we'd have:  100=60+50+35-x-2*10+0 ;

x=25 .

Therefore, 25% of Foodmart customers purchase exactly two of the products listed above.

Answer: D

Hope it helps.

ramgmat · Answer

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

zest4mba · Answer

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)

hirendhanak · Answer

@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.

mailnavin1 · Answer

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 n C) 
and P (A u B u C) = P (A) + P (B) + P (C) -   - 2(P (A n B n C))

Bunuel · Answer

My post at the link I provided above (formulae-for-3-overlapping-sets-69014.html#p729340) is exactly about this issue.

KarishmaB · Answer

Some good methods have been discussed above. Let me add a small discussion on Venn diagrams

You will not have any confusion if you visualize it. The total number of people is 100 (assume it since numbers are in %). These 100 people are spread around in the 3 circles. One person can be in only one area.

Attachment:

Ques6.jpg [ 17.57 KiB | Viewed 10801 times ]

60+50+35 (= 145) is more than 100 because
60 = the entire left top circle = the left top red part + x + z + 10.
50 = the entire right top circle = the right top red part + x + y + 10
35 = the bottom circle = the bottom red part + y + z + 10
so x, y and z are counted twice and 10 is counted thrice

45 = x + y + z + 2*10
x+ y + z = 25

OptimusPrimea1 · Answer

@Karishma:

How did you get:

"45 = x + y + z + 2*10
x+ y + z = 25"

I lost the part here..

KarishmaB · Answer

145 is 45 more than 100. Why is it 45 extra? Because x, y and z were counted twice (so they appear once extra) and 10 was counted thrice ( so it appears twice extra). check out the diagram. These extras make up the 45. In 100, there is no double/triple counting. It is equal to the actual number of people. 
That is why 45 = x + y + z + 2*10

25 = x+y+z

pqhai · Answer

I used venn diagram. Here is my solution.

ScottTargetTestPrep · Answer

We can use the formula:

Total = n(M) + n(C) + n(A) - n(exactly two) - 2 * n(all three)

100 = 60 + 50 + 35 - n(exactly two) - 2 * 10

100 = 125 - n(exactly two)

n(exactly two) = 25

Answer: D

tkorzhan18 · Answer

Hi,

Could you please explain how the problem should be modified, so we need to add and not subtract customers who purchase all three products?

Kinshook · Answer

Given: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.

Asked:If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?

109% = 60% + 50% + 35% - Exacly 2 - 2*10%

Exactly 2 = 25%

IMO D

Posted from my mobile device

bumpbot · Answer

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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

Foodmart customers regularly buy at least one of the

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Foodmart customers regularly buy at least one of the

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards