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:

Four spheres and three cubes are arranged in a line according to incre [#permalink]

Show Tags

19 Nov 2012, 13:33

9

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

50% (01:35) correct 50% (01:14) wrong based on 232 sessions

HideShow timer Statistics

Four spheres and three cubes are arranged in a line according to increasing volume, with no two solids of the same type adjacent to each other. The ratio of the volume of one solid to that of the next largest is constant. If the radius of the smallest sphere is ¼ that of the largest sphere, what is the radius of the smallest sphere?

(1) The volume of the smallest cube is 72pi. (2) The volume of the second largest sphere is 576pi.

Four spheres and three cubes are arranged in a line acc. to increasing vol. , with no two solids of the same type adjacent to each other . The ratio of the volume of one solid to that of the next largest is constant . if the radius of the smallest sphere is 1/4 of the largest sphere, what is the radius of smallest sphere? 1. Vol. of smallest cube is 72 pi . 2. Vol. of second largest sphere is 576 pi.

I'm happy to help with this.

From the prompt, we know the shapes are arranged in order of increasing volume, and the shapes are in the order: 1) sphere 2) cube 3) sphere 4) cube 5) sphere 6) cube 7) sphere

The ratios of the volumes are constant, so what we have is a geometric sequence. Call that ratio r. Let's say the volume of #1 is V. Then, the volumes are 1) sphere = V 2) cube = r*V 3) sphere = (r^2)*V 4) cube = (r^3)*V 5) sphere = (r^4)*V 6) cube = (r^5)*V 7) sphere = (r^6)*V

Then, the prompt tells us that radius of #1 is 1/4 the radius of #7. If the lengths from #1 to #7 increase by 4 times (scale factor = 4), then the volume increases by 4^3 = 64. For more on scale factors, see: http://magoosh.com/gmat/2012/scale-fact ... decreases/

In other words, (r^6)*V = 64V ----> r^6 = 64 -----> r = 2

As it happens, we were easily able to solve for the numerical value of r here. Even if that were not the case, even if r were some ugly decimal, it would be the same. At this point, we know all the ratios, and all we need is a single value, any value on the list, and that would allow us to calculate every number on the list. In other words, any value would allow us to solve for V and, since we already know r, knowing V would allow us to calculate every term.

Now, that statements: 1. Vol. of smallest cube is 72 pi . 2. Vol. of second largest sphere is 576 pi. Each statement gives us the numerical value of the volume of a specific shape in the arrangement, so each statement, all alone and by itself, will be sufficient for determining the answer to the prompt question.

That's why the OA is D

Does all this make sense?

Mike
_________________

Mike McGarry Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Re: Four spheres and three cubes are arranged in a line according to incre [#permalink]

Show Tags

19 Nov 2012, 17:31

1

This post received KUDOS

himanshuhpr wrote:

Four spheres and three cubes are arranged in a line acc. to increasing vol. , with no two solids of the same type adjacent to each other . The ratio of the volume of one solid to that of the next largest is constant . if the radius of the smallest sphere is 1/4 of the largest sphere, what is the radius of smallest sphere?

1. Vol. of smallest cube is 72 pi . 2. Vol. of second largest sphere is 576 pi.

Since there are 4 spheres and 3 cubes. Only possible way to arrange them in alternate position is possible when we have S C S C S C S Thus we know smallest in volume is sphere and largest one is also sphere and the order of placement.

Also, ratio of the volume of one solid to that of the next largest is constant. So its a GP. and from "if the radius of the smallest sphere is 1/4 of the largest sphere" we would know the ratio between volume of largest and smallest sphere and from it can deduce the ratio between any two solids.

Statement 1: Vol of smallest cube is 72pi. We know ratio between any two solids. We can find out volume of smallest sphere and thus radius. Sufficient Statement 2:Vol. of second largest sphere is 576 pi. We know ratio between any two solids. We can find out volume of smallest sphere and thus radius. Sufficient

Re: Four spheres and three cubes are arranged in a line according to incre [#permalink]

Show Tags

03 Nov 2014, 08:56

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.
_________________

Re: Four spheres and three cubes are arranged in a line according to incre [#permalink]

Show Tags

18 Jun 2016, 03:17

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.
_________________

Four spheres and three cubes are arranged in a line according to increasing volume, with no two solids of the same type adjacent to each other. The ratio of the volume of one solid to that of the next largest is constant. If the radius of the smallest sphere is ¼ that of the largest sphere, what is the radius of the smallest sphere?

(1) The volume of the smallest cube is 72pi. (2) The volume of the second largest sphere is 576pi.

Answer: Option D

Please check the solution as attached

Attachments

File comment: www.GMATinsight.com

Untitled.jpg [ 129.58 KiB | Viewed 2665 times ]

_________________

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

Re: Four spheres and three cubes are arranged in a line according to incre [#permalink]

Show Tags

26 Aug 2016, 23:14

mikemcgarry wrote:

himanshuhpr wrote:

Four spheres and three cubes are arranged in a line acc. to increasing vol. , with no two solids of the same type adjacent to each other . The ratio of the volume of one solid to that of the next largest is constant . if the radius of the smallest sphere is 1/4 of the largest sphere, what is the radius of smallest sphere? 1. Vol. of smallest cube is 72 pi . 2. Vol. of second largest sphere is 576 pi.

I'm happy to help with this.

From the prompt, we know the shapes are arranged in order of increasing volume, and the shapes are in the order: 1) sphere 2) cube 3) sphere 4) cube 5) sphere 6) cube 7) sphere

The ratios of the volumes are constant, so what we have is a geometric sequence. Call that ratio r. Let's say the volume of #1 is V. Then, the volumes are 1) sphere = V 2) cube = r*V 3) sphere = (r^2)*V 4) cube = (r^3)*V 5) sphere = (r^4)*V 6) cube = (r^5)*V 7) sphere = (r^6)*V

Then, the prompt tells us that radius of #1 is 1/4 the radius of #7. If the lengths from #1 to #7 increase by 4 times (scale factor = 4), then the volume increases by 4^3 = 64. For more on scale factors, see: http://magoosh.com/gmat/2012/scale-fact ... decreases/

In other words, (r^6)*V = 64V ----> r^6 = 64 -----> r = 2

As it happens, we were easily able to solve for the numerical value of r here. Even if that were not the case, even if r were some ugly decimal, it would be the same. At this point, we know all the ratios, and all we need is a single value, any value on the list, and that would allow us to calculate every number on the list. In other words, any value would allow us to solve for V and, since we already know r, knowing V would allow us to calculate every term.

Now, that statements: 1. Vol. of smallest cube is 72 pi . 2. Vol. of second largest sphere is 576 pi. Each statement gives us the numerical value of the volume of a specific shape in the arrangement, so each statement, all alone and by itself, will be sufficient for determining the answer to the prompt question.

That's why the OA is D

Does all this make sense?

Mike

hi mike,

how do you know sphere is the first shape in the order. Even cube might be first in the order. In the question they have just mentioned that smallest sphere radius is 1/4 the radius of largest sphere

how do you know sphere is the first shape in the order. Even cube might be first in the order. In the question they have just mentioned that smallest sphere radius is 1/4 the radius of largest sphere

Since there are no two solid of same type adjacent to each other For 4 spheres and 3 cubes be arranged so that no two spheres to be adjacent, any two consecutive spheres must be separated by a cube between them hence the arrangement will be alternate starting from a sphere.

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

Re: Four spheres and three cubes are arranged in a line according to incre [#permalink]

Show Tags

03 Sep 2017, 06:12

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.
_________________