It is currently 16 Oct 2017, 19:13

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

Three rugs have a combined area of 200 square meters. By overlapping t

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

Hide Tags

1 KUDOS received
Manager
Manager
avatar
Joined: 22 Sep 2010
Posts: 88

Kudos [?]: 214 [1], given: 0

Three rugs have a combined area of 200 square meters. By overlapping t [#permalink]

Show Tags

New post 06 Oct 2010, 06:08
1
This post received
KUDOS
15
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

73% (01:53) correct 27% (02:14) wrong based on 204 sessions

HideShow timer Statistics

Three rugs have a combined area of 200 square meters. By overlapping the rugs to cover floor area of 140 square meters, the area that is covered by exactly two layers of rug is 24 square meters. What is the area that is covered with three layers of rug ?

A. 18 square meters
B. 20 square meters
C. 24 square meters
D. 28 square meters
E. 30 square meters
[Reveal] Spoiler: OA

Kudos [?]: 214 [1], given: 0

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41875

Kudos [?]: 128460 [1], given: 12173

Re: Three rugs have a combined area of 200 square meters. By overlapping t [#permalink]

Show Tags

New post 06 Oct 2010, 06:33
1
This post received
KUDOS
Expert's post
6
This post was
BOOKMARKED
pzazz12 wrote:
Three rugs have a combined area of 200 square meters. By overlapping the rugs to cover floor area of 140 square meters, the area that is covered by exactly two layers of rug is 24 square meters. What is the area that is covered with three layers of rug ?

A. 18 square meters
B. 20 square meters
C. 24 square meters
D. 28 square meters
E. 30 square meters


Total = Rug1 + Rug2 + Rug3 - {overlap of exactly 2 rugs} - 2*{overlap of exactly 3 rugs}

140 = 200 - 24 - 2*{overlap of exactly 2 rugs} --> {overlap of exactly 3 rugs} = 18.

Answer: A.

For more about the formula used and the way it's derived see my post here: formulae-for-3-overlapping-sets-69014.html?hilit=exactly%20groups

Hope it helps.
_________________

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.


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

Kudos [?]: 128460 [1], given: 12173

1 KUDOS received
Manager
Manager
avatar
Joined: 24 Jun 2010
Posts: 140

Kudos [?]: 38 [1], given: 26

Concentration: Strategy, Technology
Reviews Badge
Re: Three rugs have a combined area of 200 square meters. By overlapping t [#permalink]

Show Tags

New post 06 Oct 2010, 11:03
1
This post received
KUDOS
2
This post was
BOOKMARKED
Bunuel wrote:
pzazz12 wrote:
Three rugs have a combined area of 200 square meters. By overlapping the rugs to cover floor area of 140 square meters, the area that is covered by exactly two layers of rug is 24 square meters. What is the area that is covered with three layers of rug ?

A. 18 square meters
B. 20 square meters
C. 24 square meters
D. 28 square meters
E. 30 square meters


Total = Rug1 + Rug2 + Rug3 - {overlap of exactly 2 rugs} - 2*{overlap of exactly 3 rugs}

140 = 200 - 24 - 2*{overlap of exactly 2 rugs} --> {overlap of exactly 3 rugs} = 18.

Answer: A.

For more about the formula used and the way it's derived see my post here: formulae-for-3-overlapping-sets-69014.html?hilit=exactly%20groups

Hope it helps.


Agree with A..

This is a triple overlapping set.

Here is how I did it (thanks for Horacio Quiroga of MGMAT for teaching me this technique)

S is the sum of just the single carpets, D is sum of double overlaps, and T is sum of the triple overlaps

S + 2D + 3T = 200 (accounts for the total area of carpets and overlaps)
S + D + T = 140 (excludes double counting)

Subtracting the equations gets me:

D + 2T = 60

I know that the total "double overlap" is 24 so I substitute in

2T = 60 - 24
T = 18

So far this technique has gotten me through all triple overlapping sets

Kudos [?]: 38 [1], given: 26

Senior Manager
Senior Manager
avatar
Joined: 12 May 2010
Posts: 289

Kudos [?]: 77 [0], given: 12

Location: United Kingdom
Concentration: Entrepreneurship, Technology
GMAT Date: 10-22-2011
GPA: 3
WE: Information Technology (Internet and New Media)
Re: Three rugs have a combined area of 200 square meters. By overlapping t [#permalink]

Show Tags

New post 13 Nov 2010, 12:15
Hi,

MGMAT advocates using Venn diagrams for triple sets ... I have no idea how to do this with Venn diagrams... can someone please help me?

Thinking in Venn diagram terms here:

I thought there are actually 3 pairs of 2 overlapping rug areas in this question (r1 overlapping r2, r2 overlapping r3, r1 overlapping r3)
and not 2? So shouldnt it be 3*24 to count all double overlaps?

And, isn't there only 1 overlap of all 3 rugs!?

Sorry but I'm thoroughly confused here

Thanks

Kudos [?]: 77 [0], given: 12

Expert Post
3 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7667

Kudos [?]: 17315 [3], given: 232

Location: Pune, India
Re: Three rugs have a combined area of 200 square meters. By overlapping t [#permalink]

Show Tags

New post 13 Nov 2010, 19:34
3
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
n2739178 wrote:
Hi,

MGMAT advocates using Venn diagrams for triple sets ... I have no idea how to do this with Venn diagrams... can someone please help me?

Thinking in Venn diagram terms here:

I thought there are actually 3 pairs of 2 overlapping rug areas in this question (r1 overlapping r2, r2 overlapping r3, r1 overlapping r3)
and not 2? So shouldnt it be 3*24 to count all double overlaps?

And, isn't there only 1 overlap of all 3 rugs!?

Sorry but I'm thoroughly confused here

Thanks


Venn Diagram:
I have given a letter to each region to clarify.
Attachment:
Ques1.jpg
Ques1.jpg [ 16.36 KiB | Viewed 5856 times ]

Rug 1 + Rug 2 + Rug 3 = 200
(a + x + y + k) + (b + x + k + z) + (c + y + k + z) = 200

But area of floor covered is only 140 i.e. if each section is counted only once
a + b + c + x + y + z + k = 140
Subtracting second equation from first, x + y + z + 2k = 60
But x + y + z (Area with two layers of rug) = 24
So 2k = 36 or k = 18
This is how it can be done using a venn diagram.

Note: You obviously wouldn't need to make all these equations and can directly jump to x + y + z + 2k = 60 but I wrote them down for clarity. It is really hard to say 'Section of Rug 1 which is in single layer..section of rug 2 in two layers etc'
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17315 [3], given: 232

Senior Manager
Senior Manager
avatar
Joined: 12 May 2010
Posts: 289

Kudos [?]: 77 [0], given: 12

Location: United Kingdom
Concentration: Entrepreneurship, Technology
GMAT Date: 10-22-2011
GPA: 3
WE: Information Technology (Internet and New Media)
Re: Three rugs have a combined area of 200 square meters. By overlapping t [#permalink]

Show Tags

New post 14 Nov 2010, 04:05
wow that is awesome! I didn't realise you could simply solve using equations like that. This has clarified this 100% for me! thanks!

Kudos [?]: 77 [0], given: 12

Senior Manager
Senior Manager
avatar
Joined: 12 May 2010
Posts: 289

Kudos [?]: 77 [0], given: 12

Location: United Kingdom
Concentration: Entrepreneurship, Technology
GMAT Date: 10-22-2011
GPA: 3
WE: Information Technology (Internet and New Media)
Re: Three rugs have a combined area of 200 square meters. By overlapping t [#permalink]

Show Tags

New post 14 Nov 2010, 04:11
actually - how would you jump directly to x + y + z + 2k = 60 without writing the equations?

Kudos [?]: 77 [0], given: 12

Expert Post
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7667

Kudos [?]: 17315 [0], given: 232

Location: Pune, India
Re: Three rugs have a combined area of 200 square meters. By overlapping t [#permalink]

Show Tags

New post 14 Nov 2010, 05:58
n2739178 wrote:
actually - how would you jump directly to x + y + z + 2k = 60 without writing the equations?


It is again a matter of thinking vs solving. If I think more, I have to solve less.
Combined area of rugs is 200 sq m while area of floor they cover is only 140 sq m. So what does the extra 60 sq m do? It covers another rug!
Wherever there are two rugs overlapping, one rug is not covering the floor but just another rug.
Wherever there are three rugs overlapping, two rugs are not covering the floor but just the third rug at the bottom.
so can I say that x + y + z is the area where one rug is covering another rug and k is the area where two rugs are covering another rug?
or put another way, can I say x + y + z + 2k = 60?

This entire 'thinking process' takes ten seconds once you are comfortable with it and your answer would be out in 30 sec flat!
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17315 [0], given: 232

Intern
Intern
avatar
Joined: 17 Jun 2015
Posts: 10

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

Re: Three rugs have a combined area of 200 square meters. By overlapping t [#permalink]

Show Tags

New post 18 Jun 2015, 00:00
I am new here from Melbourne, Australia and trying to solve as many questions as I can for my test. I am looking or more rugs type questions.
_________________

Rugs online Australia

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

Expert Post
SVP
SVP
User avatar
G
Joined: 08 Jul 2010
Posts: 1834

Kudos [?]: 2272 [0], given: 51

Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: Three rugs have a combined area of 200 square meters. By overlapping t [#permalink]

Show Tags

New post 18 Jun 2015, 00:04
PaulShep wrote:
I am new here from Melbourne, Australia and trying to solve as many questions as I can for my test. I am looking or more rugs type questions.


Hi paul,

Please refer to the links below:

search.php?search_tags=all&selected_search_tags%5B%5D=65&selected_search_tags%5B%5D=216

search.php?search_tags=all&selected_search_tags%5B%5D=65&selected_search_tags%5B%5D=187

search.php?search_tags=all&selected_search_tags%5B%5D=65&selected_search_tags%5B%5D=217


For any specific catagory of Questions please be guided by the directory

gmat-ps-question-directory-by-topic-difficulty-127957.html
ds-question-directory-by-topic-difficulty-128728.html

I hope it helps!
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Kudos [?]: 2272 [0], given: 51

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41875

Kudos [?]: 128460 [0], given: 12173

Re: Three rugs have a combined area of 200 square meters. By overlapping t [#permalink]

Show Tags

New post 18 Jun 2015, 01:29
PaulShep wrote:
I am new here from Melbourne, Australia and trying to solve as many questions as I can for my test. I am looking or more rugs type questions.



Theory on Overlapping Sets:
advanced-overlapping-sets-problems-144260.html
how-to-draw-a-venn-diagram-for-problems-98036.html

All DS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=45
All PS Overlapping Sets Problems to practice: search.php?search_id=tag&tag_id=65


Hope it helps.
_________________

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.


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

Kudos [?]: 128460 [0], given: 12173

Intern
Intern
avatar
Joined: 17 Jun 2015
Posts: 10

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

Re: Three rugs have a combined area of 200 square meters. By overlapping t [#permalink]

Show Tags

New post 21 Jun 2015, 23:04
Thanks, these are really helping1
_________________

Rugs online Australia

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

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16795

Kudos [?]: 273 [0], given: 0

Premium Member
Re: Three rugs have a combined area of 200 square meters. By overlapping t [#permalink]

Show Tags

New post 30 Sep 2017, 00:18
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 273 [0], given: 0

Re: Three rugs have a combined area of 200 square meters. By overlapping t   [#permalink] 30 Sep 2017, 00:18
Display posts from previous: Sort by

Three rugs have a combined area of 200 square meters. By overlapping t

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


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

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

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®.