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:

You are given an unlimited number of circles each of which [#permalink]

Show Tags

11 Jan 2013, 01:20

7

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

59% (02:57) correct
41% (01:40) wrong based on 113 sessions

HideShow timer Statistics

You are given an unlimited number of circles each of which having radii either 2 or 4. You must place the circles side-by-side so that they only touch at one point. If exactly two of the smaller circles are used, in how many different ways may the circles be placed next to one another so that the centers of the circles are all on the same straight line and so that the sum of the lengths of the diameters of the circles is 32?

Re: You are given an unlimited number of circles each of which [#permalink]

Show Tags

11 Jan 2013, 02:38

1

This post received KUDOS

MOKSH wrote:

You are given an unlimited number of circles each of which having radii either 2 or 4 .you must place the circles side-by-side so that they only touch at one point. If exactly two of the smaller circles are used, in how many different ways may the circles be placed next to one another so that the centers of the circles are all on the same straight line and so that the sum of the lengths of the diameters of the circles is 32? four six eight ten twelve

We need to have following combination 1) 2 circles of radii 2 2) 3 circle of radii 4 Now...arrangements of N things in which p and q items are similar to each other. 5! / (3!*2!) 10
_________________

You are given an unlimited number of circles each of which having radii either 2 or 4. You must place the circles side-by-side so that they only touch at one point. If exactly two of the smaller circles are used, in how many different ways may the circles be placed next to one another so that the centers of the circles are all on the same straight line and so that the sum of the lengths of the diameters of the circles is 32?

A. four B. six C. eight D. ten E. twelve

The the sum of the lengths of the diameters of two smaller circles is 2*4=8. Hence, the sum sum of the lengths of the diameters of larger circles is 32-8=24, which means that there should be 24/8=3 large circles.

So, we have that there should be 2 small circles and 3 large circles.

The number of arrangement is 5!/(3!*2!)=10 (the number of arrangements of 5 objects in a row, where 3 of the objects are identical and the remaining 2 objects are identical as well).

Re: You are given an unlimited number of circles each of which [#permalink]

Show Tags

11 Jan 2013, 05:23

1

This post was BOOKMARKED

MOKSH wrote:

You are given an unlimited number of circles each of which having radii either 2 or 4. You must place the circles side-by-side so that they only touch at one point. If exactly two of the smaller circles are used, in how many different ways may the circles be placed next to one another so that the centers of the circles are all on the same straight line and so that the sum of the lengths of the diameters of the circles is 32?

A. four B. six C. eight D. ten E. twelve

Got me a little confused a bit with this statement: "If exactly two of the smaller circles are used" because I'm not a native speaker but then yeah 2 smaller circles and the rest are bigger circles....

2 smaller circles will have sum of length of diameter = 8

\(32-8 = 24\) remaining diameter for the larger circles of diameter 8, Thus, 3 larger circles.

Re: You are given an unlimited number of circles each of which [#permalink]

Show Tags

11 Jan 2013, 07:43

Large circle has a diameter of 8, Small circle has a diameter of 4. Since total length of diameters must be 32 and exactly 2 smaller circles are used ---> There are 3 large circles and 2 small circles (for a total of 5 circles) that need to be arraged. Therefore.. (5!)/(3!)(2!) = 10 (D)

You are given an unlimited number of circles each of which is identical to one of the two circles shown above. The radii of the larger circles are 4 and the radii of the smaller circles are 2. You must place the circles side-by-side so that they only touch at one point. If exactly two of the smaller circles are used, in how many different ways may the circles be placed next to one another so that the centers of the circles are all on the same straight line and so that the sum of the lengths of the diameters of the circles is 32?

A. four B. six C. eight D. ten E. Twelve
_________________

ISB Class of 2017 | ISB Preparation Kit ____________________________________________________________________________________________________________________________________________________ ISB Class of 2016 | GMAT Retake Debrief ____________________________________________________________________________________________________________________________________________________ ISB Class of 2015 | GMAT Debrief ____________________________________________________________________________________________________________________________________________________

Last edited by ankurgupta03 on 21 Jun 2013, 07:40, edited 1 time in total.

You are given an unlimited number of circles each of which is identical to one of the two circles shown above. The radii of the larger circles are 4 and the radii of the smaller circles are 2. You must place the circles side-by-side so that they only touch at one point. If exactly two of the smaller circles are used, in how many different ways may the circles be placed next to one another so that the centers of the circles are all on the same straight line and so that the sum of the lengths of the diameters of the circles is 32?

A. four B. six C. eight D. ten E. Twelve

I just don't get it, can some one please help. I cannot see any one of the given options to be correct. Will post my reasoning once i receive a method to derive the answer

You are given an unlimited number of circles each of which is identical to one of the two circles shown above. The radii of the larger circles are 4 and the radii of the smaller circles are 2. You must place the circles side-by-side so that they only touch at one point. If exactly two of the smaller circles are used, in how many different ways may the circles be placed next to one another so that the centers of the circles are all on the same straight line and so that the sum of the lengths of the diameters of the circles is 32?

A. four B. six C. eight D. ten E. Twelve

I just don't get it, can some one please help. I cannot see any one of the given options to be correct. Will post my reasoning once i receive a method to derive the answer

Sorry for that Bunnel, i tried searching the question, but somehow did not find it
_________________

ISB Class of 2017 | ISB Preparation Kit ____________________________________________________________________________________________________________________________________________________ ISB Class of 2016 | GMAT Retake Debrief ____________________________________________________________________________________________________________________________________________________ ISB Class of 2015 | GMAT Debrief ____________________________________________________________________________________________________________________________________________________

You are given an unlimited number of circles each of which is identical to one of the two circles shown above. The radii of the larger circles are 4 and the radii of the smaller circles are 2. You must place the circles side-by-side so that they only touch at one point. If exactly two of the smaller circles are used, in how many different ways may the circles be placed next to one another so that the centers of the circles are all on the same straight line and so that the sum of the lengths of the diameters of the circles is 32?

A. four B. six C. eight D. ten E. Twelve

I just don't get it, can some one please help. I cannot see any one of the given options to be correct. Will post my reasoning once i receive a method to derive the answer

Sorry for that Bunnel, i tried searching the question, but somehow did not find it

No worries. Just please name a topic properly when posting: the name of the topic must be the first sentence of the question or a string of words exactly as they show up in the question.

Re: You are given an unlimited number of circles each of which [#permalink]

Show Tags

28 Jan 2016, 06:50

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.
_________________

Even if you don't know the 'technical math' behind this question, you can still get to the correct answer with a little bit of 'brute force' work.

From the prompt, you can deduce that we'll need 2 small circles and 3 large circles to complete the task. From the answer choices, we know that there can only be 4, 6, 8, 10 or 12 ways to arrange those 5 circles, so it shouldn't be that tough to 'map out' the possibilities.

After days of waiting, sharing the tension with other applicants in forums, coming up with different theories about invites patterns, and, overall, refreshing my inbox every five minutes to...

I was totally freaking out. Apparently, most of the HBS invites were already sent and I didn’t get one. However, there are still some to come out on...

In early 2012, when I was working as a biomedical researcher at the National Institutes of Health , I decided that I wanted to get an MBA and make the...