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

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Math Expert
Joined: 02 Sep 2009
Posts: 59632
What is the maximum number of 4x4x4 cubes that can fit in a rectangula  [#permalink]

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20 Sep 2019, 05:08
00:00

Difficulty:

45% (medium)

Question Stats:

49% (01:06) correct 51% (01:05) wrong based on 91 sessions

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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

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Joined: 20 Aug 2017
Posts: 55
Re: What is the maximum number of 4x4x4 cubes that can fit in a rectangula  [#permalink]

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20 Sep 2019, 05:20
Bunuel wrote:
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

It is more of a HCF question as we need to find the maximum number that can fit in 10x12x16.
The number of cubes that can fit in 10x12x16 =
(10x12x16)/(4x4x4) = 30 cubes.

If you like my solution, do give kudos!
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Joined: 11 Jun 2019
Posts: 34
Location: India
Re: What is the maximum number of 4x4x4 cubes that can fit in a rectangula  [#permalink]

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20 Sep 2019, 05:41
IMO (D).
10/4 = 2 (plus some fraction)
12/4 = 3
16/4 = 4
Hence 2x3x4=24

Posted from my mobile device
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Re: What is the maximum number of 4x4x4 cubes that can fit in a rectangula  [#permalink]

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20 Sep 2019, 05:43
1
Bunuel wrote:
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

We need to find maximum number of 4x4x4 cubes that can fully fit in 10x12x16 rectangular box
=> number of cube boxes * volume of cubes=volume of rectangular box

Let number of boxes be n

=>n * 4x4x4 = 10x12x16

=> n= $$\frac{10 * 12 * 16}{4 * 4 * 4}$$

Notice that only 12(4*3) and 16(4*4) are divisible by 4. $$\frac{10}{4}$$ = 2.5. How can 2.5 cube boxes fit? So maximum number of boxes ≠ 30 (trap answer)

So instead of 2.5, only 2 boxes can fit.

Therefore, maximum number of boxes = 2 * 3 * 4 = 24..........option D
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Re: What is the maximum number of 4x4x4 cubes that can fit in a rectangula  [#permalink]

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20 Sep 2019, 08:38
1
possiblities of max cubes which can fit in a box ;
10/4 ; 2
12/4 ; 3
16/4 ; 4
2*3*4 ; 24
IMO D

Bunuel wrote:
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
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3158
What is the maximum number of 4x4x4 cubes that can fit in a rectangula  [#permalink]

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Updated on: 29 Sep 2019, 04:32

Solution

To find:
• The maximum number of 4 x 4 x 4 cubes that can fit in a rectangular box measuring 10 x 12 x 16

Approach and Working Out:
• Volume of the box = 10 * 12 * 16 = 1920
• Volume of a cube = 4 * 4 * 4 = 64
However, 10 is not divisible by 4 and 10= 2.5. So, at max 2 cubes can fit in one side.

Therefore, maximum number of cubes = $$\frac{10*12*16}{4*4*4} = 2* 3* 4 = 24$$

Hence, the correct answer is Option D.

_________________

Originally posted by EgmatQuantExpert on 23 Sep 2019, 13:22.
Last edited by EgmatQuantExpert on 29 Sep 2019, 04:32, edited 2 times in total.
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Joined: 05 May 2019
Posts: 143
GPA: 3
Re: What is the maximum number of 4x4x4 cubes that can fit in a rectangula  [#permalink]

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26 Sep 2019, 07:22
I'm afraid that's incorrect EgmatQuantExpert hehe.
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Re: What is the maximum number of 4x4x4 cubes that can fit in a rectangula  [#permalink]

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26 Sep 2019, 11:10
Bunuel wrote:
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

Let us assume 16 - length , 12 - breadth and 10 - height of the rectangular box in which the cube of side 4 are to be fitted.

So along the length we can place = 16/4 = 4 cubes

Along the breadth we can place = 12/4 = 3 cubes

Along the height we can place = 10/4 = 2.5 Hence 2 cubes

So maximum number of cubes that can fit = 4*3*2 = 24 cubes (D)
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Joined: 04 Jan 2015
Posts: 3158
Re: What is the maximum number of 4x4x4 cubes that can fit in a rectangula  [#permalink]

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29 Sep 2019, 04:34
Re: What is the maximum number of 4x4x4 cubes that can fit in a rectangula   [#permalink] 29 Sep 2019, 04:34
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