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:

The interior of a rectangular carton is designed by a certai [#permalink]

Show Tags

25 Feb 2011, 07:24

2

This post received KUDOS

6

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

64% (04:31) correct
36% (02:56) wrong based on 141 sessions

HideShow timer Statistics

The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3:2:2. In terms of x, which of the following equals the height of the carton, in feet?

A. 3√x B. 3√[(2x)/3] C. 3√[(3x)/2] D. (2/3) 3√x E. (3/2) 3√x

The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3:2:2. In terms of x, which of the following equals the height of the carton, in feet?

A. 3√x B. 3√[(2x)/3] C. 3√[(3x)/2] D. (2/3) 3√x E. (3/2) 3√x

Given: \(length:width:height=3k:2k:2k\), for some positive number \(k\). Also: \(volume=x=3k*2k*2k\) --> \(x=12k^3\) --> \(k=\sqrt[3]{\frac{x}{12}}\) --> \(height=2k=\sqrt[3]{\frac{2x}{3}}\).

Re: The interior of a rectangular carton is designed by a certai [#permalink]

Show Tags

22 Dec 2013, 10:23

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: The interior of a rectangular carton is designed by a certai [#permalink]

Show Tags

26 Sep 2015, 09:15

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: The interior of a rectangular carton is designed by a certai [#permalink]

Show Tags

13 Mar 2016, 05:00

Expert's post

Viktoriaa wrote:

Hi Bunuel,

Could you suggest any way to master these questions? I seem to know how to deal with them, but make silly mistakes every single time.

Thanks!

Hi, It will be important to know at what stage do you go wrong.. 1)formula stage.. 2)calculations.. 3)difficulty with variables..

For example in this Qs.. things one should know. 1)formula for Volume of RECTANGULAR BOX.. 2) converting ratio 3:2:2 to numeric values by multiplying each term by common variable.. 3) What one has to be careful is to realize a) it is not square root but 3rd root b) height is 2 * variable ..

the other way to do is to take same value for common term in ratio. find the volume.. work backwards by substituting V in choices to get height.

Re: The interior of a rectangular carton is designed by a certai [#permalink]

Show Tags

13 Mar 2016, 07:59

Hi, It will be important to know at what stage do you go wrong.. 1)formula stage.. 2)calculations.. 3)difficulty with variables..

For example in this Qs.. things one should know. 1)formula for Volume of RECTANGULAR BOX.. 2) converting ratio 3:2:2 to numeric values by multiplying each term by common variable.. 3) What one has to be careful is to realize a) it is not square root but 3rd root b) height is 2 * variable ..

the other way to do is to take same value for common term in ratio. find the volume.. work backwards by substituting V in choices to get height. [/quote]

Hi,

Thanks a lot for such a detailed reply! I think I just go wrong with recognizing equations themselves - I mean, in this case, I new formula of the volume and paid attention to some tricky parts, but didn't use variable in 3:2:2... Probably just need more attention....

Re: The interior of a rectangular carton is designed by a certai [#permalink]

Show Tags

16 Mar 2016, 15:57

Bunuel wrote:

naaga wrote:

The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3:2:2. In terms of x, which of the following equals the height of the carton, in feet?

A. 3√x B. 3√[(2x)/3] C. 3√[(3x)/2] D. (2/3) 3√x E. (3/2) 3√x

Given: \(length:width:height=3k:2k:2k\), for some positive number \(k\). Also: \(volume=x=3k*2k*2k\) --> \(x=12k^3\) --> \(k=\sqrt[3]{\frac{x}{12}}\) --> \(height=2k=\sqrt[3]{\frac{2x}{3}}\).

Answer: B.

confused how you got from : \(k=\sqrt[3]{\frac{x}{12}}\) --> \(height=2k=\sqrt[3]{\frac{2x}{3}}\). can you break this down further please?

Re: The interior of a rectangular carton is designed by a certai [#permalink]

Show Tags

16 Mar 2016, 19:45

Expert's post

1

This post was BOOKMARKED

sagnik242 wrote:

Bunuel wrote:

naaga wrote:

The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3:2:2. In terms of x, which of the following equals the height of the carton, in feet?

A. 3√x B. 3√[(2x)/3] C. 3√[(3x)/2] D. (2/3) 3√x E. (3/2) 3√x

Given: \(length:width:height=3k:2k:2k\), for some positive number \(k\). Also: \(volume=x=3k*2k*2k\) --> \(x=12k^3\) --> \(k=\sqrt[3]{\frac{x}{12}}\) --> \(height=2k=\sqrt[3]{\frac{2x}{3}}\).

Answer: B.

confused how you got from : \(k=\sqrt[3]{\frac{x}{12}}\) --> \(height=2k=\sqrt[3]{\frac{2x}{3}}\). can you break this down further please?

Hi, \(k=\sqrt[3]{\frac{x}{12}}\) .. height is 2k as ratios are 3k:2k:2k so \(2k=2\sqrt[3]{\frac{x}{12}}\).. => \(2k=\sqrt[3]{8}\sqrt[3]{\frac{x}{12}}\).. \(2k=\sqrt[3]{\frac{8x}{12}}\).. \(height=2k=\sqrt[3]{\frac{2x}{3}}\).. hope this is what you were looking for _________________

Re: The interior of a rectangular carton is designed by a certai [#permalink]

Show Tags

05 May 2016, 04:59

naaga wrote:

The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3:2:2. In terms of x, which of the following equals the height of the carton, in feet?

A. 3√x B. 3√[(2x)/3] C. 3√[(3x)/2] D. (2/3) 3√x E. (3/2) 3√x

We are given that the ratio of length: width: height = 3 : 2 : 2 and we are also given that the volume of the rectangular solid is x. We can use n as the variable multiplier for our ratio, giving us:

length: width: height = 3n : 2n : 2n

Now we are ready to determine the height in terms of x.

Answer: B _________________

Jeffrey Miller Jeffrey Miller Head of GMAT Instruction

http://blog.ryandumlao.com/wp-content/uploads/2016/05/IMG_20130807_232118.jpg The GMAT is the biggest point of worry for most aspiring applicants, and with good reason. It’s another standardized test when most of us...

I recently returned from attending the London Business School Admits Weekend held last week. Let me just say upfront - for those who are planning to apply for the...