It is currently 20 Oct 2017, 21:39

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Suppose five circles, each 4 inches in diameter, are cut from a rectan

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

Hide Tags

Senior Manager
Senior Manager
User avatar
Joined: 03 Mar 2010
Posts: 422

Kudos [?]: 361 [0], given: 22

Schools: Simon '16 (M)
Suppose five circles, each 4 inches in diameter, are cut from a rectan [#permalink]

Show Tags

New post 14 Sep 2011, 12:27
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

55% (01:47) correct 45% (01:57) wrong based on 176 sessions

HideShow timer Statistics

Suppose five circles, each 4 inches in diameter, are cut from a rectangular strip of paper 12 inches long. If the least amount of paper is to be wasted, what is the width of the paper strip?

(A) 5
(B) 4+2\(\sqrt{3}\)
(C) 8
(D) 4(1+\(\sqrt{3}\))
(E) 12
[Reveal] Spoiler: OA

_________________

My dad once said to me: Son, nothing succeeds like success.

Kudos [?]: 361 [0], given: 22

4 KUDOS received
Intern
Intern
avatar
Joined: 10 May 2011
Posts: 22

Kudos [?]: 9 [4], given: 0

Location: India
Concentration: Strategy, General Management
GMAT 1: 690 Q50 V32
Re: Suppose five circles, each 4 inches in diameter, are cut from a rectan [#permalink]

Show Tags

New post 14 Sep 2011, 19:49
4
This post received
KUDOS
Well, don't know how to draw diagrams here but let me see if i can explain through text.

First Approach (Traditional): First place 3 circles back-to-back (touching each other) to make it for 12 inches length. Now for least wastage of paper, you need to put 4th and 5th circles above 3 circles. 4th between 1st and 2nd circles and 5th between 2nd and 3rd. Now you can make equilateral triangle by joining centers of 1st, 2nd, and 4th circles. So total width of the strip will be radius of 4th cricle + height of equilateral triangle + radius of 1st (or 2nd) circle. It equals 2 + (sqrt3/2)4 + 2 = 4 + 2sqrt3

Second approach (quicker): Just think, if we place 4th circle exactly on the top of the 1st circle width of the strip will be sum of diameters of 2 circles 1.e 8. But that is not the case. Since 4th circle is placed between 1st and 2nd, some part of their diameters will overlap. It means our answer should be less than 8. You can eliminate options (C), (D), and (E). Option (A) is too less a value (it is suggesting that 4th circle is actually fitting 3/4th of its diameter between 1st and 2nd circles, which is not feasible). So you are left with only option and that's your answer.

I hope it helps!!!

Kudos [?]: 9 [4], given: 0

Intern
Intern
avatar
Status: Mission MBA
Joined: 02 Jul 2010
Posts: 43

Kudos [?]: 15 [0], given: 5

Location: Hyderabad, India
Schools: ISB, IIMs
Re: Suppose five circles, each 4 inches in diameter, are cut from a rectan [#permalink]

Show Tags

New post 14 Sep 2011, 23:20
hiimmunish wrote:
Well, don't know how to draw diagrams here but let me see if i can explain through text.

First Approach (Traditional): First place 3 circles back-to-back (touching each other) to make it for 12 inches length. Now for least wastage of paper, you need to put 4th and 5th circles above 3 circles. 4th between 1st and 2nd circles and 5th between 2nd and 3rd. Now you can make equilateral triangle by joining centers of 1st, 2nd, and 4th circles. So total width of the strip will be radius of 4th cricle + height of equilateral triangle + radius of 1st (or 2nd) circle. It equals 2 + (sqrt3/2)4 + 2 = 4 + 2sqrt3

Second approach (quicker): Just think, if we place 4th circle exactly on the top of the 1st circle width of the strip will be sum of diameters of 2 circles 1.e 8. But that is not the case. Since 4th circle is placed between 1st and 2nd, some part of their diameters will overlap. It means our answer should be less than 8. You can eliminate options (C), (D), and (E). Option (A) is too less a value (it is suggesting that 4th circle is actually fitting 3/4th of its diameter between 1st and 2nd circles, which is not feasible). So you are left with only option and that's your answer.

I hope it helps!!!



Good Explanation !! hiimmunish keep it up!!
_________________

If you find my posts useful, Appreciate me with the kudos!! +1

Kudos [?]: 15 [0], given: 5

Senior Manager
Senior Manager
User avatar
Joined: 03 Mar 2010
Posts: 422

Kudos [?]: 361 [0], given: 22

Schools: Simon '16 (M)
Re: Suppose five circles, each 4 inches in diameter, are cut from a rectan [#permalink]

Show Tags

New post 15 Sep 2011, 00:19
@hiimmunish I like your second (quicker) approach.
Kudos to you.

Thanks.
_________________

My dad once said to me: Son, nothing succeeds like success.

Kudos [?]: 361 [0], given: 22

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16637

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

Premium Member
Re: Suppose five circles, each 4 inches in diameter, are cut from a rectan [#permalink]

Show Tags

New post 11 Sep 2014, 14:36
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

Expert Post
6 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7676

Kudos [?]: 17370 [6], given: 232

Location: Pune, India
Re: Suppose five circles, each 4 inches in diameter, are cut from a rectan [#permalink]

Show Tags

New post 11 Sep 2014, 22:35
6
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
jamifahad wrote:
Suppose five circles, each 4 inches in diameter, are cut from a rectangular strip of paper 12 inches long. If the least amount of paper is to be wasted, what is the width of the paper strip?

(A) 5
(B) 4+2\(\sqrt{3}\)
(C) 8
(D) 4(1+\(\sqrt{3}\))
(E) 12


First, think what they mean by 'least amount of paper is to be wasted'? Since the dimension of the circles is given, perhaps what they mean is that the width of the paper used must be minimum since the leftover paper will be wasted. So how will you place the 5 circles? The diameter of the circles is 4 each and the length of the paper is 12 so you can place 3 circles neatly across the length. The other two must be placed in a way which reduces width of the paper, which means between two circles rather than edge to edge.

Attachment:
Ques4.jpg
Ques4.jpg [ 23.97 KiB | Viewed 1474 times ]

Once the diagram is ready, the solution is self explanatory. The equilateral triangle in the middle has side 4 because the sides are formed by 2 radii. The width of the paper is the sum of dashed lines, the regular ones are 2 each (radii of circles) and the bold one is the altitude of the equilateral triangle \(= \sqrt{3}*4/2 = 2*\sqrt{3}\).

So width \(= 2 + 2*\sqrt{3} + 2 = 4 + 2*\sqrt{3}\)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17370 [6], given: 232

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1853

Kudos [?]: 2626 [0], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Suppose five circles, each 4 inches in diameter, are cut from a rectan [#permalink]

Show Tags

New post 12 Sep 2014, 01:40
Unless I saw the diagram, the question was not easy as writing on the wall...

Thanks Karishma +Kudos to you
_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2626 [0], given: 193

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16637

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

Premium Member
Re: Suppose five circles, each 4 inches in diameter, are cut from a rectan [#permalink]

Show Tags

New post 21 Jan 2017, 13:34
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

Manager
Manager
User avatar
S
Status: Math Tutor
Joined: 12 Aug 2017
Posts: 72

Kudos [?]: 29 [0], given: 13

WE: Education (Education)
Suppose five circles, each 4 inches in diameter, are cut from a rectan [#permalink]

Show Tags

New post 23 Aug 2017, 12:43
If we are cutting five circles each with radius of 2, their total area is 5*4*pi which is slightly greater than 60.
Length of Strip = 12
So breadth should be more than 5. Since least paper is wasted
Option A: Wrong
Option B: Most suitable
Option C: Bigger then option B
Option D: Bigger than option B
Option E: Bigger than option B
_________________

Abhishek Parikh
Math Tutor
Whatsapp- +919983944321
Mobile- +971529685639
Website: http://www.holamaven.com

Kudos [?]: 29 [0], given: 13

Suppose five circles, each 4 inches in diameter, are cut from a rectan   [#permalink] 23 Aug 2017, 12:43
Display posts from previous: Sort by

Suppose five circles, each 4 inches in diameter, are cut from a rectan

  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®.