GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 27 May 2020, 00:05 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A rectanglar cuboid with dimensions 6 x12 x 15 is cut into Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Director  Joined: 07 Jun 2004
Posts: 542
Location: PA
A rectanglar cuboid with dimensions 6 x12 x 15 is cut into  [#permalink]

### Show Tags

1
A rectanglar cuboid with dimensions 6 x12 x 15 is cut into exact number of equal cubes . What will be the least number of cubes.
Intern  Joined: 06 Sep 2004
Posts: 44
Re: A rectanglar cuboid with dimensions 6 x12 x 15 is cut into  [#permalink]

### Show Tags

2*4*5= 40 cubes.

size of each cbe = 3 X 3
Manager  Joined: 28 Aug 2004
Posts: 176
Re: A rectanglar cuboid with dimensions 6 x12 x 15 is cut into  [#permalink]

### Show Tags

1
Should be 6.

Total surface area = 684.

6s^2*n = 684, where n is the least number of cubes
s^2*n = 114

prime factorization of 114 = 6 * 19

(sqrt(19))^2 * 6 = 114

n = 6.

Originally posted by Dan on 08 Jan 2005, 21:43.
Last edited by Dan on 09 Jan 2005, 08:22, edited 1 time in total.
Director  Joined: 25 Nov 2004
Posts: 976
Re: A rectanglar cuboid with dimensions 6 x12 x 15 is cut into  [#permalink]

### Show Tags

rxs0005 wrote:
A rectanglar cuboid with dimensions 6 x12 x 15 is cut into exact number of equal cubes . What will be the least number of cubes.

cut the rectangular cubide solid with 3 x 3 x 3 size. if we cut the solid with these dimensions, there will be 40 cubes. this is the least number of equal cubes. more than this we can make 1x1x1 dimensions equal 1080 cubes as well.
Manager  Joined: 20 Dec 2004
Posts: 185
Re: A rectanglar cuboid with dimensions 6 x12 x 15 is cut into  [#permalink]

### Show Tags

Side of each cube = n
Total number of cubes = k

6*12*15 = n^3 * k

k = 1080/n^3

Now all we need to do is have a max possible value of n that will result in a integer k.

n = 2, k = non integer

n = 3, k = 40

n = 4, k = non integer

n = 5, k = non integer

n = 6 , k = non integer

n = 7 , k = non integer

n = 8, k = non integer

n = 9 , k = non integer

n > 9 , k < 1

Moreover the choices if there are any would drive the answer

regards
Manager  Joined: 28 Aug 2004
Posts: 176
Re: A rectanglar cuboid with dimensions 6 x12 x 15 is cut into  [#permalink]

### Show Tags

maybe I am wrong, but we're interested in this question in the total surface area of the cuboid rather than in its volume since we want to 'cut' it rather than 'fill' it.
Manager  Joined: 30 Dec 2004
Posts: 229
Location: California
Re: A rectanglar cuboid with dimensions 6 x12 x 15 is cut into  [#permalink]

### Show Tags

I get 5 cubes as the least number of cubes that you can get from a 6x12x15 rectangular cuboid:

Did the problem similar to neelesh:

k = 1080/n^3 = (6x12x15)/n^3 = (2*3*2*2*3*3*5)/n^3 = (6^3*5)/n^3

when n = 6 k = 5...could be wrong though...whats the OA?
Intern  Joined: 08 Jan 2005
Posts: 6
Re: A rectanglar cuboid with dimensions 6 x12 x 15 is cut into  [#permalink]

### Show Tags

Hi. I think it should be 40 cubes.

Since, we are looking at the least no. of same sized cubes, we are now looking for the max. volume of a cube that can be cut equally.

Now looking at the dimension of cuboid : 6*12* 15 , the max. side that can be cut will be gcd of 6,12 and 15 which is 3. This implies that the max. side of the cube will be 3 with a max. volume of 27.

Total volume of the cuboid = 1080

So the max. no. of cubes of the same side will be 1080/27 = 40
Intern  Joined: 09 Jan 2005
Posts: 11
Re: A rectanglar cuboid with dimensions 6 x12 x 15 is cut into  [#permalink]

### Show Tags

I think the answer is 5 cubes with a side of 6.
( will explain if my answer is correct)
Director  Joined: 18 Nov 2004
Posts: 929
Re: A rectanglar cuboid with dimensions 6 x12 x 15 is cut into  [#permalink]

### Show Tags

5 cubes for me.

6x12x15 = nx^3 where n is number of cubes and x cube dimension.

2^3*3^3*5 = nx^3

For n to be least x3 has to be max....we get that for n = 5 and

x^3 = 2^3*3^3

x===> 6
Director  Joined: 07 Jun 2004
Posts: 542
Location: PA
Re: A rectanglar cuboid with dimensions 6 x12 x 15 is cut into  [#permalink]

### Show Tags

Since we want to find out the least number of cubes then we should get the largest cube that can be made so highest common factor of the dimensions of 6 12 15 thats 3 so each cube will be volume 3^3 = 27

Total cubes = 6 * 12 * 15 / 27 = 40

rxs0005
Director  Joined: 18 Nov 2004
Posts: 929
Re: A rectanglar cuboid with dimensions 6 x12 x 15 is cut into  [#permalink]

### Show Tags

Why is it not x(side) = 6, which will give you a lesser no of cubes i.e. 5 as I explained earlier ?
Manager  Joined: 31 Aug 2004
Posts: 111
Re: A rectanglar cuboid with dimensions 6 x12 x 15 is cut into  [#permalink]

### Show Tags

neelesh wrote:
Side of each cube = n
Total number of cubes = k

6*12*15 = n^3 * k

k = 1080/n^3

Now all we need to do is have a max possible value of n that will result in a integer k.

n = 2, k = non integer

n = 3, k = 40

n = 4, k = non integer

n = 5, k = non integer

n = 6 , k = non integer

n = 7 , k = non integer

n = 8, k = non integer

n = 9 , k = non integer

n > 9 , k < 1

Moreover the choices if there are any would drive the answer

regards

When n = 6, k=5. So the least number of cube is 5.

rxs0005, is OA = 40?
Senior Manager  Joined: 21 Sep 2004
Posts: 338
Re: A rectanglar cuboid with dimensions 6 x12 x 15 is cut into  [#permalink]

### Show Tags

i get it now. been understanding less number of cubes.. its the other way around.
Manager  Joined: 31 Aug 2004
Posts: 111
Re: A rectanglar cuboid with dimensions 6 x12 x 15 is cut into  [#permalink]

### Show Tags

The answer is not 5 cubes with each side = 6. Is that because for the side of 15, we cannot cut it to exact number? ie 15/6 is not an integer?

For the cubes with side = 3, each side can be divided into an integer. ie 6, 12, 15 /3 = 2, 4, 5

If so I would agree with the answer 40.
Manager  Joined: 30 Dec 2004
Posts: 229
Location: California
Re: A rectanglar cuboid with dimensions 6 x12 x 15 is cut into  [#permalink]

### Show Tags

I still do not understand why 5 is not the answer. They are asking for the least number of cubes. If you divide 1080/6^3 you get 5, that is less thatn 40 and isn't that the question, the least number of cubes you can get? I think the OA is wrong!
Intern  Joined: 09 Jan 2005
Posts: 11
A rectanglar cuboid with dimensions 6 x12 x 15 is cut into  [#permalink]

### Show Tags

The cube has to be cut exactly. I made a mistake in stating that 5 is the answer.

If the cube is of dimensions 6^3, you would get only 4 cubes and not 5 . The fifth one will be of dimensions 3*6*12. This is leftover, a cuboid, and so 4 as answer cannot satisfy the question's condition. A rectanglar cuboid with dimensions 6 x12 x 15 is cut into   [#permalink] 15 Jan 2005, 21:44

# A rectanglar cuboid with dimensions 6 x12 x 15 is cut into Question banks Downloads My Bookmarks Reviews Important topics  