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

 It is currently 22 Oct 2018, 18:03

### 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

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

# What is the maximum number of 4x4x4 cubes that can fit in a

Author Message
Senior Manager
Joined: 05 Jun 2005
Posts: 429
What is the maximum number of 4x4x4 cubes that can fit in a  [#permalink]

### Show Tags

03 Nov 2006, 23:01
3
10
00:00

Difficulty:

45% (medium)

Question Stats:

57% (00:50) correct 43% (00:32) wrong based on 288 sessions

### HideShow timer Statistics

What is the maximum number of 4x4x4 cubes that can fit in a rectangular box measuring 10x12x16 ?

A. 12
B. 18
C. 20
D. 24
E. 30

M23-06
Manager
Joined: 03 Jul 2005
Posts: 187
Location: City

### Show Tags

Updated on: 06 Nov 2006, 00:46
I go for 30. I multiplied 4 x 4 x 4 = 64 and 10 x 12 x 16 = 1920. 64 can only go 30 times into 1920.

Originally posted by lfox2 on 04 Nov 2006, 00:54.
Last edited by lfox2 on 06 Nov 2006, 00:46, edited 1 time in total.
Intern
Joined: 06 Sep 2006
Posts: 25

### Show Tags

04 Nov 2006, 03:34
2
1
I go for 24

the 10x12x16 rectangular box fits for 24 4x4x4 cubs.

Dimensions of the rectangular box are not all perfectly divisible by 4(cube Dimensions) so there must be an empty part in the box, since 10 is not divisible by 4.
==> Therefore we pretend that the box rectangle is 8x12x16, with a total area of 1536. ===>1536/64=24
Senior Manager
Joined: 24 Oct 2006
Posts: 334

### Show Tags

04 Nov 2006, 05:50
1
I went with 16/4 (4) * 12/4 (3) * 10/4 (apparently 2 cubes) = 24

(or say how many cubes fit on each side)
Retired Moderator
Joined: 05 Jul 2006
Posts: 1727

### Show Tags

04 Nov 2006, 06:23
assuming that the base of th recatngle = 12*16 = 192

the maximum one level cubes = 12 ie: (192/16)

hight = 10 ( 4*2+2) so it can take two levels of the cubes = 12*2 = 24

assuming base of rectangle = 16*10 = 160

the maximum one level cubes = 160/16 = 10

hight is 12 = 4*3 so it can take three levels of cubes with hight 4

maximum number of cubes = 30

Manager
Joined: 01 Nov 2006
Posts: 70

### Show Tags

04 Nov 2006, 06:50
Nope. Check out ezo's fine solution. You are figuring out volume and squishing your boxes.
Senior Manager
Joined: 01 Oct 2006
Posts: 485

### Show Tags

04 Nov 2006, 09:34
yezz wrote:
assuming that the base of th recatngle = 12*16 = 192

the maximum one level cubes = 12 ie: (192/16)

hight = 10 ( 4*2+2) so it can take two levels of the cubes = 12*2 = 24

assuming base of rectangle = 16*10 = 160

the maximum one level cubes = 160/16 = 10

hight is 12 = 4*3 so it can take three levels of cubes with hight 4

maximum number of cubes = 30

Here in second case we can not have more than 8 cubes in each row.
You can only 4 along the length i.e16 and 2 along the width that is 10.
Thus no will be 8. So max will be 24.
Please correct me if I am wrong.
Director
Joined: 01 Feb 2011
Posts: 668

### Show Tags

16 Sep 2011, 20:54
1
side with length 16

number of segments of length 4 we can fit on this side <= 16/4
=> maximum = 4

side with length 12

number of segments of length 4 we can fit on this side <= 12/4 = 3
=> maximum = 3

side with length 10

number of segments of length 4 we can fit on this side <= 10/4 = 2

=> maximum = 2

=> maximum number of cubes with length 4 that can be fit in a rectangular box of dimensions 16,12,10
= 4*3*2 = 24
Manager
Joined: 20 Nov 2010
Posts: 161

### Show Tags

18 Sep 2011, 00:14
Its 24.
(10/4) * (12/4) * ( 16/4) = 24.
_________________

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
MGMAT 6 650 (51,31) on 31/8/11
MGMAT 1 670 (48,33) on 04/9/11
MGMAT 2 670 (47,34) on 07/9/11
MGMAT 3 680 (47,35) on 18/9/11
GMAT Prep1 680 ( 50, 31) on 10/11/11

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
CR notes
http://gmatclub.com/forum/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142
http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133
http://gmatclub.com/forum/gmat-prep-critical-reasoning-collection-106783.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html
http://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html?hilit=chineseburned

Senior Manager
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 488
Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Re: What is the maximum number of 4x4x4 cubes that can fit in a  [#permalink]

### Show Tags

06 Mar 2014, 13:41
Bunuel, I still believe that this Could some how be solved by LCM and HCF logic.

_________________

Like my post Send me a Kudos It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

Manager
Joined: 01 May 2013
Posts: 61
Re: What is the maximum number of 4x4x4 cubes that can fit in a  [#permalink]

### Show Tags

06 Mar 2014, 15:08
honchos wrote:
Bunuel, I still believe that this Could some how be solved by LCM and HCF logic.

That honestly seems like overkill. Just picture a box. You'd try to fill it as efficiently as you could. So you'd start packing on the 12x16 side, so 3x4 = 12 boxes. How many stacks of 12? 10/4 = 2.5, so there are 2 full stacks. 12x2 = 24.

12 x 16 x 10 --> 3*4*2 = 24 is the fastest way to do this problem.
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1829
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: What is the maximum number of 4x4x4 cubes that can fit in a  [#permalink]

### Show Tags

06 Mar 2014, 19:32
9
2
$$\frac{(10 * 12 * 16)}{(4 * 4 * 4)}$$

$$\frac{12}{4} = 3$$

$$\frac{16}{4} = 4$$

$$\frac{10}{4} = 2$$ max (We cant do a decimal calculation here; cannot adjust dimensions of the boxes; so max quotient is 2)

Answer = 4 x 2 x 3 = 24 = D
_________________

Kindly press "+1 Kudos" to appreciate

Senior Manager
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 488
Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Re: What is the maximum number of 4x4x4 cubes that can fit in a  [#permalink]

### Show Tags

06 Mar 2014, 22:01
PareshGmat wrote:
$$\frac{(10 * 12 * 16)}{(4 * 4 * 4)}$$

$$\frac{12}{4} = 3$$

$$\frac{16}{4} = 4$$

$$\frac{10}{4} = 2$$ max (We cant do a decimal calculation here; cannot adjust dimensions of the boxes; so max quotient is 2)

Answer = 4 x 2 x 3 = 24 = D

Yes that is a far better approach, I think you have used that LCM/HCF concept, Isn't it.

Do you remember the relationship between HCF/LCM
_________________

Like my post Send me a Kudos It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

Manager
Joined: 01 May 2013
Posts: 61
Re: What is the maximum number of 4x4x4 cubes that can fit in a  [#permalink]

### Show Tags

06 Mar 2014, 22:49
honchos wrote:
CCMBA wrote:
honchos wrote:
Bunuel, I still believe that this Could some how be solved by LCM and HCF logic.

That honestly seems like overkill. Just picture a box. You'd try to fill it as efficiently as you could. So you'd start packing on the 12x16 side, so 3x4 = 12 boxes. How many stacks of 12? 10/4 = 2.5, so there are 2 full stacks. 12x2 = 24.

12 x 16 x 10 --> 3*4*2 = 24 is the fastest way to do this problem.
Go and sit in actual exam, exam will tell you what honestly kills any one. Better and time saving approach's are thumbs up in the real Examination.

Your answer doesn't make sense, Just a rat race marathon. Every can and has solved it by that method.

But this question can certainly be solve through LCM/HCF.

This is not a "rat race marathon" as you suggest. I'm pretty sure you're the one who's trying to look for a harder, more time-consuming solution. My visual was meant to concretize the problem, which you seemed to have trouble understanding. When I did this, I used the exact approach many are advocating: Divide each dimension by 4. Multiply the integer parts of the quotient.

So 12/4 * 16/4 * 10/4 becomes 3*4*2. I did this in 30 seconds. On my paper, I had 7 numbers written down: first row (12, 16, 10), second row (3, 4, 2, 24). Just because someone takes the time to explain her logic does not mean she doesn't understand how to get the answer. I think about how to do the problem. There was really no need to insult me. If you cannot tell this is the exact same method others have proposed, it speaks to an inability to recognize and apply concepts when they are presented to you in a novel format. That appears to be your problem.
Intern
Joined: 03 Mar 2014
Posts: 11
Re: What is the maximum number of 4x4x4 cubes that can fit in a  [#permalink]

### Show Tags

06 Mar 2014, 22:56
1
I just drew it out on paper. 12 cubes per level (I made the base 12x16 bc both are div by 4) and 2 levels of cubes.

So 24
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1829
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: What is the maximum number of 4x4x4 cubes that can fit in a  [#permalink]

### Show Tags

06 Mar 2014, 23:04
1
honchos wrote:
PareshGmat wrote:
$$\frac{(10 * 12 * 16)}{(4 * 4 * 4)}$$

$$\frac{12}{4} = 3$$

$$\frac{16}{4} = 4$$

$$\frac{10}{4} = 2$$ max (We cant do a decimal calculation here; cannot adjust dimensions of the boxes; so max quotient is 2)

Answer = 4 x 2 x 3 = 24 = D

Yes that is a far better approach, I think you have used that LCM/HCF concept, Isn't it.

Do you remember the relationship between HCF/LCM

Not used HCF/LCM. Cant recall the relation

In this type of question, the learning lesson for me is that we cannot "adjust" the dimensions given. So 10/4 max can yield 2 as quotient; cannot "borrow" from the adjacent nos. at make it a perfect division.

Its a nice problem.
_________________

Kindly press "+1 Kudos" to appreciate

Senior Manager
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 488
Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Re: What is the maximum number of 4x4x4 cubes that can fit in a  [#permalink]

### Show Tags

06 Mar 2014, 23:07
CCMBA,

What you are trying to preach me even I could solve by that method or rather any one who is preparing for GMAT can solve by this method.

But GMAT is far beyond you comprehension as rumor mongers always rumor's that quantitative questions are quite easy.

I have given the GMAT and scored 710. Q50 V36

As soon as you keep on doing all the questions correctly the difficulty level continue to rise and one questions pops up, which were even far difficult then CAT one's. One question, I will not post it as it against policy, could be solved only by the use of Binomial theorem.

You are continuously arguing for a method , which was already discussed on this threads and ON many threads before. There seems no logic you are TRYING TO PREACH ME THE the same method what was discussed before in the thread.

My idea of posting is to enrich the Post not to clutter it with the same methods, which are already in place.

Neither do I post just for the sake of posting.

All those who believes GMAT quant is easy, make sure that GMAT writers are smartest people on earth and they will check down to bottom before the give you Q51.

Life is like Boomerang you send insult, it will come back to you as an insult. you TRIED TO PLAY OVER-SMART BY THESE WORDS-
That honestly seems like overkill.

If you are too possessive in your comfort Zone and do not want to diversify the learning process, it seems you are infatuated with your frog well.

I simply requested Bunuel to intervene, instead you did, infact you can, But you just repeat the same method, which every one on thos Forum Knows and initiated a insulting and sarcastic language-
That honestly seems like overkill.

If you cant handle sarcasm, better you should drop it application on others.
_________________

Like my post Send me a Kudos It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

Senior Manager
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 488
Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Re: What is the maximum number of 4x4x4 cubes that can fit in a  [#permalink]

### Show Tags

06 Mar 2014, 23:11
PareshGmat wrote:
honchos wrote:
PareshGmat wrote:
$$\frac{(10 * 12 * 16)}{(4 * 4 * 4)}$$

$$\frac{12}{4} = 3$$

$$\frac{16}{4} = 4$$

$$\frac{10}{4} = 2$$ max (We cant do a decimal calculation here; cannot adjust dimensions of the boxes; so max quotient is 2)

Answer = 4 x 2 x 3 = 24 = D

Yes that is a far better approach, I think you have used that LCM/HCF concept, Isn't it.

Do you remember the relationship between HCF/LCM

Not used HCF/LCM. Cant recall the relation

In this type of question, the learning lesson for me is that we cannot "adjust" the dimensions given. So 10/4 max can yield 2 as quotient; cannot "borrow" from the adjacent nos. at make it a perfect division.

Its a nice problem.

Thanks Paresh, we all know that trick, but my point was to learn some arithmetic approach that may have broad application in other questions also.
_________________

Like my post Send me a Kudos It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

Manager
Joined: 01 May 2013
Posts: 61
Re: What is the maximum number of 4x4x4 cubes that can fit in a  [#permalink]

### Show Tags

08 Mar 2014, 09:56
honchos wrote:
CCMBA,

What you are trying to preach me even I could solve by that method or rather any one who is preparing for GMAT can solve by this method.

But GMAT is far beyond you comprehension as rumor mongers always rumor's that quantitative questions are quite easy.

I have given the GMAT and scored 710. Q50 V36

As soon as you keep on doing all the questions correctly the difficulty level continue to rise and one questions pops up, which were even far difficult then CAT one's. One question, I will not post it as it against policy, could be solved only by the use of Binomial theorem.

You are continuously arguing for a method , which was already discussed on this threads and ON many threads before. There seems no logic you are TRYING TO PREACH ME THE the same method what was discussed before in the thread.

My idea of posting is to enrich the Post not to clutter it with the same methods, which are already in place.

Neither do I post just for the sake of posting.

All those who believes GMAT quant is easy, make sure that GMAT writers are smartest people on earth and they will check down to bottom before the give you Q51.

Life is like Boomerang you send insult, it will come back to you as an insult. you TRIED TO PLAY OVER-SMART BY THESE WORDS-
That honestly seems like overkill.

If you are too possessive in your comfort Zone and do not want to diversify the learning process, it seems you are infatuated with your frog well.

I simply requested Bunuel to intervene, instead you did, infact you can, But you just repeat the same method, which every one on thos Forum Knows and initiated a insulting and sarcastic language-
That honestly seems like overkill.

If you cant handle sarcasm, better you should drop it application on others.

The GMAT is in part a reasoning test. You have to pick the best method in a giving situation. I only explained why this was the best method. Overkill = too much work. That wasn't meant to be an insult. Your response, however, was deliberately insulting. Both times.

Furthermore, you could simply look up the LCM/HCF method, which no one seems to remember. That way people might have a better idea of how to answer your question. And don't have to risk being attacked while doing it.

Stop being rude.
Senior Manager
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 488
Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Re: What is the maximum number of 4x4x4 cubes that can fit in a  [#permalink]

### Show Tags

08 Mar 2014, 10:36
CCMBA wrote:
honchos wrote:
CCMBA,

What you are trying to preach me even I could solve by that method or rather any one who is preparing for GMAT can solve by this method.

But GMAT is far beyond you comprehension as rumor mongers always rumor's that quantitative questions are quite easy.

I have given the GMAT and scored 710. Q50 V36

As soon as you keep on doing all the questions correctly the difficulty level continue to rise and one questions pops up, which were even far difficult then CAT one's. One question, I will not post it as it against policy, could be solved only by the use of Binomial theorem.

You are continuously arguing for a method , which was already discussed on this threads and ON many threads before. There seems no logic you are TRYING TO PREACH ME THE the same method what was discussed before in the thread.

My idea of posting is to enrich the Post not to clutter it with the same methods, which are already in place.

Neither do I post just for the sake of posting.

All those who believes GMAT quant is easy, make sure that GMAT writers are smartest people on earth and they will check down to bottom before the give you Q51.

Life is like Boomerang you send insult, it will come back to you as an insult. you TRIED TO PLAY OVER-SMART BY THESE WORDS-
That honestly seems like overkill.

If you are too possessive in your comfort Zone and do not want to diversify the learning process, it seems you are infatuated with your frog well.

I simply requested Bunuel to intervene, instead you did, infact you can, But you just repeat the same method, which every one on thos Forum Knows and initiated a insulting and sarcastic language-
That honestly seems like overkill.

If you cant handle sarcasm, better you should drop it application on others.

The GMAT is in part a reasoning test. You have to pick the best method in a giving situation. I only explained why this was the best method. Overkill = too much work. That wasn't meant to be an insult. Your response, however, was deliberately insulting. Both times.

Furthermore, you could simply look up the LCM/HCF method, which no one seems to remember. That way people might have a better idea of how to answer your question. And don't have to risk being attacked while doing it.

Stop being rude.

If you are sitting for GMAT and do not about LCM/HCF you need to revise your topic list.
You will certainly get drilled at Data sufficiency.

If acknowledging your beliefs is a rude phenomenon to you then I do not have any party in it.

Take away:
LCM/HCF is a tested Phenomenon in GMAT examination. Gmatclub.com has lots many questions on that.

some times in exam and some times is life, difficult method is the only method shortcuts, tricks and reasoning has their limits, and you have to learn it hard way, if you really want to enter into the ruthless and cruel world of MBA'S and management.

Solving 1000's questions doesn't make sense. 200 questions well solved and solved with learning of all the possible tested concepts will do the needful.

I have seen this attitude first time in the FORUM.

If you will write anything personal further I will not have party in that.

Boss, You do not seems to be receptive. No Grudges I am moving on. All the best.
_________________

Like my post Send me a Kudos It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

Re: What is the maximum number of 4x4x4 cubes that can fit in a &nbs [#permalink] 08 Mar 2014, 10:36

Go to page    1   2    Next  [ 21 posts ]

Display posts from previous: Sort by