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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

14 Sep 2011, 11:27

6

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

57% (01:48) correct 43% (01:49) wrong based on 161 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?

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

Show Tags

14 Sep 2011, 18:49

5

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.

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?

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 [ 23.97 KiB | Viewed 1623 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 \(= \sqrt{3}*4/2 = 2*\sqrt{3}\).

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

Show Tags

23 Aug 2017, 11:43

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- +971568653827 Website: http://www.holamaven.com