GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 09 Dec 2019, 20:03

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

The interior of a rectangular carton is designed by a certain

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 19 Sep 2010
Posts: 9
The interior of a rectangular carton is designed by a certain  [#permalink]

Show Tags

New post Updated on: 16 May 2017, 04:25
13
1
95
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

72% (02:29) correct 28% (02:47) wrong based on 1822 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. \(\sqrt[3]{x}\)

B. \(\sqrt[3]{\frac{2x}{3}}\)

C. \(\sqrt[3]{\frac{3x}{2}}\)

D. \(\frac{2}{3}*\sqrt[3]{x}\)

E. \(\frac{3}{2}*\sqrt[3]{x}\)

Originally posted by naaga on 25 Feb 2011, 07:24.
Last edited by Bunuel on 16 May 2017, 04:25, edited 1 time in total.
Edited the question.
Most Helpful Expert Reply
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8292
Re: The interior of a rectangular carton is designed by a certain  [#permalink]

Show Tags

New post 16 Mar 2016, 19:45
26
17
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
_________________
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59622
The interior of a rectangular carton is designed by a certain  [#permalink]

Show Tags

New post 25 Feb 2011, 08:04
23
13
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. \(\sqrt[3]{x}\)

B. \(\sqrt[3]{\frac{2x}{3}}\)

C. \(\sqrt[3]{\frac{3x}{2}}\)

D. \(\frac{2}{3}*\sqrt[3]{x}\)

E. \(\frac{3}{2}*\sqrt[3]{x}\)


Given: \(length:width:height=3k:2k:2k\), for some positive number \(k\).

Also: \(volume=x=3k*2k*2k\);

\(x=12k^3\);

\(k^3=\frac{x}{12}\);

\(k=\sqrt[3]{\frac{x}{12}}\);

\(height=2k=\sqrt[3]{\frac{2x}{3}}\).

Answer: B.
_________________
Most Helpful Community Reply
Intern
Intern
avatar
Joined: 23 Mar 2016
Posts: 24
Schools: Tulane '18 (M$)
Re: The interior of a rectangular carton is designed by a certain  [#permalink]

Show Tags

New post 04 May 2016, 21:45
3
3
Simple plug and play here

Choose the numbers given (3:2:2) = 12 for volume. Then, plug 12 into X in the answer choices to get 2.

cuberoot(2x/3) > cuberoot(2(12)/3) > cuberoot(24/3) > cuberoot (8) > 2

I immediately started with B, since it makes since (to find V, it'll be a cuberoot of something, with some division involved), and blamo it worked.
General Discussion
Manager
Manager
User avatar
Joined: 17 Feb 2011
Posts: 143
Concentration: Real Estate, Finance
Schools: MIT (Sloan) - Class of 2014
GMAT 1: 760 Q50 V44
Re: The interior of a rectangular carton is designed by a certain  [#permalink]

Show Tags

New post 25 Feb 2011, 07:49
2
Picking numbers:

If l = 3, w = 2 and h = 2, volume = 12.

Now, testing:

sq rt 12 = 2* sq rt 3 = approx 2*1.73 = approx 3.46
A) 3* sq rt 12 = approx 10.4 WRONG
B) 3 *sq rt 8 = approx 3 * 2.8 = 8.4 WRONG
C) 3 * sq rt 18 = approx 3 * 3*sq rt 2 = 3 * 4.2 = 12.6 WRONG
D) (2/3) * 3.46 = approx 2.3
E) (3/2) * 3.46 = approx 5.1

I would choose D, but it is not exact. Did I do anything wrong?
E)
Intern
Intern
avatar
Joined: 02 Feb 2016
Posts: 13
Re: The interior of a rectangular carton is designed by a certain  [#permalink]

Show Tags

New post 13 Mar 2016, 04:46
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!
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8292
Re: The interior of a rectangular carton is designed by a certain  [#permalink]

Show Tags

New post 13 Mar 2016, 05:00
1
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.

_________________
Manager
Manager
avatar
Joined: 28 Dec 2013
Posts: 65
Re: The interior of a rectangular carton is designed by a certain  [#permalink]

Show Tags

New post 16 Mar 2016, 15:57
3
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?
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: The interior of a rectangular carton is designed by a certain  [#permalink]

Show Tags

New post 05 May 2016, 04:59
11
8
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.

Image

Answer: B
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Manager
Manager
avatar
B
Joined: 10 Sep 2014
Posts: 75
Location: Bangladesh
GPA: 3.5
WE: Project Management (Manufacturing)
Re: The interior of a rectangular carton is designed by a certain  [#permalink]

Show Tags

New post 17 Mar 2018, 00:31
How x=12k to the power 3 becomes k= Cube root x/12? chetan2u Bunuel please help. I understood the later part of the problem. Thanks.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59622
The interior of a rectangular carton is designed by a certain  [#permalink]

Show Tags

New post 17 Mar 2018, 03:18
Intern
Intern
avatar
B
Joined: 25 Mar 2018
Posts: 4
Re: The interior of a rectangular carton is designed by a certain  [#permalink]

Show Tags

New post 05 May 2018, 06:42
1
1
chetan2u wrote:
sagnik242 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?[/quote]

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[/quote]


How does 2k become: \(\sqrt[3]{8}\sqrt[3]{\frac{x}{12}}\)..
Where you get the 8 from?
Intern
Intern
avatar
B
Joined: 17 May 2019
Posts: 19
Re: The interior of a rectangular carton is designed by a certain  [#permalink]

Show Tags

New post 29 Jul 2019, 13:09
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. \(\sqrt[3]{x}\)

B. \(\sqrt[3]{\frac{2x}{3}}\)

C. \(\sqrt[3]{\frac{3x}{2}}\)

D. \(\frac{2}{3}*\sqrt[3]{x}\)

E. \(\frac{3}{2}*\sqrt[3]{x}\)


Given: \(length:width:height=3k:2k:2k\), for some positive number \(k\).

Also: \(volume=x=3k*2k*2k\);

\(x=12k^3\);

\(k^3=\frac{x}{12}\);

\(k=\sqrt[3]{\frac{x}{12}}\);

\(height=2k=\sqrt[3]{\frac{2x}{3}}\).

Answer: B.


Hi Bunuel

Thanks for your reply.

Do you mind clarifying the red part? Thank you very much
VP
VP
User avatar
D
Joined: 14 Feb 2017
Posts: 1314
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GMAT 3: 650 Q47 V33
GMAT 4: 650 Q44 V36
GMAT 5: 650 Q48 V31
GMAT 6: 600 Q38 V35
GPA: 3
WE: Management Consulting (Consulting)
Reviews Badge CAT Tests
Re: The interior of a rectangular carton is designed by a certain  [#permalink]

Show Tags

New post 17 Sep 2019, 20:25
Kudos to Jeff. The only expert who explained the last step and really the only step that made this problem challenging.
VP
VP
User avatar
D
Joined: 14 Feb 2017
Posts: 1314
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GMAT 3: 650 Q47 V33
GMAT 4: 650 Q44 V36
GMAT 5: 650 Q48 V31
GMAT 6: 600 Q38 V35
GPA: 3
WE: Management Consulting (Consulting)
Reviews Badge CAT Tests
Re: The interior of a rectangular carton is designed by a certain  [#permalink]

Show Tags

New post 17 Sep 2019, 20:28
glt13 wrote:
Simple plug and play here

Choose the numbers given (3:2:2) = 12 for volume. Then, plug 12 into X in the answer choices to get 2.

cuberoot(2x/3) > cuberoot(2(12)/3) > cuberoot(24/3) > cuberoot (8) > 2

I immediately started with B, since it makes since (to find V, it'll be a cuberoot of something, with some division involved), and blamo it worked.



Just to note this works with only multiples of the ratios given.

E.g. here you used 3n:2n:2n
n= 1

n=2 3(2):2(2):2(2)
6:4:4 and volume of 96
plug 96 into the solutions to get 4
Manager
Manager
avatar
S
Joined: 18 Apr 2019
Posts: 87
Location: India
GMAT 1: 720 Q48 V40
GPA: 4
Re: The interior of a rectangular carton is designed by a certain  [#permalink]

Show Tags

New post 28 Sep 2019, 01:50
For anyone who still might be confused. Here is a simpler way and quite frankly how i go about problems involving ratios.

Given : l:b:h = 3n:2n:2n and vol=x
Asked to find length in terms of x.

From the start convert whatever you need to find to unitary. This will make your life much easier and also help you avoid silly mistakes wherein you forget to multiply your answer by some factor to get the right answer.
Getting back...

Now, l:b:h = (3/2)n : n : n

l*b*h = x
(3/2)n*n*n = x
i guess i don't need to tell you how to solve for n now.
Straight B
Manager
Manager
User avatar
B
Joined: 19 Jan 2018
Posts: 84
Re: The interior of a rectangular carton is designed by a certain  [#permalink]

Show Tags

New post 26 Nov 2019, 20:08
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. \(\sqrt[3]{x}\)

B. \(\sqrt[3]{\frac{2x}{3}}\)

C. \(\sqrt[3]{\frac{3x}{2}}\)

D. \(\frac{2}{3}*\sqrt[3]{x}\)

E. \(\frac{3}{2}*\sqrt[3]{x}\)


Let's plug numbers in!

We know that Length*Width*Height = Volume (Volume = X in this question)
And that the ratio of Length:Width: Height is 3k:2k:2k, K being a constant.
If K = 1, the volume is 12 and the Height is 2. So from the answer choices, we need to find an answer choice when you plug in x =12, you get 2. Only B does so

Answer is B
GMAT Club Bot
Re: The interior of a rectangular carton is designed by a certain   [#permalink] 26 Nov 2019, 20:08
Display posts from previous: Sort by

The interior of a rectangular carton is designed by a certain

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne