GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 06 Jul 2020, 19:39

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Foodmart customers regularly buy at least one of the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 09 Feb 2010
Posts: 39
Foodmart customers regularly buy at least one of the  [#permalink]

Show Tags

New post 02 Sep 2010, 07:47
7
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

76% (01:37) correct 24% (02:18) wrong based on 168 sessions

HideShow timer Statistics

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
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 65014
Re: Foodmart customers regularly buy at least one of the  [#permalink]

Show Tags

New post 02 Sep 2010, 08:19
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: http://gmatclub.com/forum/formulae-for- ... 69014.html

Hope it helps.
_________________
Intern
Intern
avatar
Joined: 21 Aug 2009
Posts: 33
Re: Foodmart customers regularly buy at least one of the  [#permalink]

Show Tags

New post 02 Sep 2010, 08:26
1
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
Intern
Intern
avatar
Joined: 09 Feb 2010
Posts: 39
Re: Foodmart customers regularly buy at least one of the  [#permalink]

Show Tags

New post 03 Sep 2010, 10:07
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)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 65014
Foodmart customers regularly buy at least one of the  [#permalink]

Show Tags

New post 21 Sep 2010, 23:11
4
Retired Moderator
avatar
Joined: 03 Aug 2010
Posts: 156
Re: Foodmart customers regularly buy at least one of the  [#permalink]

Show Tags

New post 23 Dec 2010, 21:51
@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.
Manager
Manager
avatar
Status: swimming against the current
Joined: 24 Jul 2009
Posts: 123
Location: Chennai, India
Re: Foodmart customers regularly buy at least one of the  [#permalink]

Show Tags

New post 25 Dec 2010, 18:59
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))
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 65014
Re: Foodmart customers regularly buy at least one of the  [#permalink]

Show Tags

New post 25 Dec 2010, 23:41
1
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.
_________________
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 10634
Location: Pune, India
Re: Foodmart customers regularly buy at least one of the  [#permalink]

Show Tags

New post 11 Oct 2011, 22:07
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
Ques6.jpg [ 17.57 KiB | Viewed 2616 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
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Manager
avatar
Joined: 09 Jun 2011
Posts: 75
Re: Foodmart customers regularly buy at least one of the  [#permalink]

Show Tags

New post 12 Oct 2011, 22:48
@Karishma:

How did you get:

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

I lost the part here..
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 10634
Location: Pune, India
Foodmart customers regularly buy at least one of the  [#permalink]

Show Tags

New post 13 Oct 2011, 07:46
OptimusPrimea1 wrote:
@Karishma:

How did you get:

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

I lost the part here..


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
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Retired Moderator
User avatar
Joined: 15 Jun 2012
Posts: 968
Location: United States
Re: Foodmart customers regularly buy at least one of the  [#permalink]

Show Tags

New post 29 Mar 2013, 23:32
4
I used venn diagram. Here is my solution.
Attachments

Untitled.jpg
Untitled.jpg [ 57.32 KiB | Viewed 6022 times ]

Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11043
Location: United States (CA)
Re: Foodmart customers regularly buy at least one of the  [#permalink]

Show Tags

New post 03 Apr 2020, 07:33
zest4mba 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%

M03-07

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
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
225 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

GMAT Club Bot
Re: Foodmart customers regularly buy at least one of the   [#permalink] 03 Apr 2020, 07:33

Foodmart customers regularly buy at least one of the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne