Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

It is currently 29 May 2017, 19:51

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

M03 Q7

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Manager
Manager
avatar
B
Joined: 14 Dec 2011
Posts: 76
Followers: 0

Kudos [?]: 54 [0], given: 74

Reviews Badge CAT Tests
M03 Q7 [#permalink]

Show Tags

New post 19 Jan 2013, 13:29
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%

Can anyone please explain the underlined part of the following formula:-
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}

Why we have multiplied 2 with {customers who by exactly 3 products} and subtracted by {customer who buy exactly 2 products} ?

Looking forward to your replies.

Thanks & Regards
Vinni
1 KUDOS received
Current Student
User avatar
Joined: 27 Jun 2012
Posts: 412
Concentration: Strategy, Finance
Followers: 86

Kudos [?]: 841 [1] , given: 184

Re: M03 Q7 [#permalink]

Show Tags

New post 19 Jan 2013, 14:05
1
This post received
KUDOS
Attachment:
Overlapping sets.jpg
Overlapping sets.jpg [ 38.52 KiB | Viewed 1035 times ]


Your doubt: Why we have multiplied 2 with {customers who by exactly 3 products} and subtracted by {customer who buy exactly 2 products} ?
-- This is because Once you add up "{customers who buy milk}+{customers who buy chicken}+{customers who buy apples}" you are already double counting {customer who buy exactly 2 products} and triple counting {customers who by exactly 3 products}. Hence you subtract the additional ones.

Let’s analyze above based on what is provided in the problem. Assume total food mart customers as 100.
{customers who buy milk}+{customers who buy chicken}+{customers who buy apples} = 60 + 50 + 35 = 145

In our diagram, it can be represented as
(a + d + g + e) + (b + d + g + f) + (c + e + g + f) = 145
(a + b + c + d + e + f + g) + (d + e + f) + 2g = 145
From the diagram, a + b + c + d + e + f + g = 100
100 + (d + e + f) + 2g = 145
100 = 145 - (d + e + f) - 2g
i.e. 100 = (milk customers + chicken customers + apple customers) - (customers who buy exactly 2 products) - 2 * (customers who buy exactly 3 products)
-- This answers your doubt.

Now lets solve the problem further
100 = 145 - (d + e + f) - 2g
(d + e + f) + 2g = 45
We know g=10,
Hence, customers who purchase exactly 2 products = (d + e + f) = 25

Thus choice(D) is the answer
_________________

Thanks,
Prashant Ponde

Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7
Reading Comprehension notes: Click here
VOTE GMAT Practice Tests: Vote Here
PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here
Looking to finance your tuition: Click here


Last edited by PrashantPonde on 19 Jan 2013, 14:10, edited 1 time in total.
Expert Post
1 KUDOS received
Math Expert
User avatar
P
Joined: 02 Sep 2009
Posts: 39062
Followers: 7756

Kudos [?]: 106580 [1] , given: 11628

Re: M03 Q7 [#permalink]

Show Tags

New post 19 Jan 2013, 14:09
1
This post received
KUDOS
Expert's post
vinnik 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%

Can anyone please explain the underlined part of the following formula:-
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}

Why we have multiplied 2 with {customers who by exactly 3 products} and subtracted by {customer who buy exactly 2 products} ?

Looking forward to your replies.

Thanks & Regards
Vinni


See detailed explanation of the formula in "ADVANCED OVERLAPPING SETS" chapter of Math Book: advanced-overlapping-sets-problems-144260.html

Hope it helps.
_________________

New to the Math Forum?
Please read this: 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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
B
Joined: 14 Dec 2011
Posts: 76
Followers: 0

Kudos [?]: 54 [0], given: 74

Reviews Badge CAT Tests
Re: M03 Q7 [#permalink]

Show Tags

New post 20 Jan 2013, 11:03
Thanks PraPon for this nice and detailed explanation. This particular concept has now become easier to understand.
And Bunuel, thanks for the link.

Appreciate your replies.

Regards
Vinni
Re: M03 Q7   [#permalink] 20 Jan 2013, 11:03
    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic M03 Q 36 icandy 20 18 Sep 2012, 08:54
50 Experts publish their posts in the topic M03 #23 redbeanaddict 18 23 Jul 2013, 03:36
1 M03 #6 dczuchta 9 21 Sep 2011, 20:22
22 M03 #01 dczuchta 27 20 Apr 2014, 06:48
3 Experts publish their posts in the topic M03 #19 jjhko 18 10 May 2014, 05:50
Display posts from previous: Sort by

M03 Q7

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

Moderator: Bunuel



GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.