Rectangular cube Diagram

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[email protected]: Master | Next Rank: 500 Posts; Posts: 429; Joined: Wed Sep 19, 2012 11:38 pmFollowed by: 4 members; Thanked: 6 times

by [email protected] » Mon Jul 14, 2014 10:37 pm

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

12

18

20

24

30

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Source: Beat The GMAT — Problem Solving | Mon Jul 14, 2014 10:37 pm

phanikpk: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Fri Jun 06, 2014 11:48 pmFollowed by: 1 member

by phanikpk » Tue Jul 15, 2014 12:35 am

Maximum number of cubes

Volume of all the cubes= volume of the rectangular box

n(4*4*4)= 10*12*16

Finally, n= 30

IMO E

Please give me OA

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by [email protected] » Tue Jul 15, 2014 12:48 am

Hi shibsriz,

This question comes with a "twist"; the rectangular box will NOT be completely filled with cubes (the dimensions won't allow for it to be filled).

The dimensions are 10x12x16, so both the 12 and 16 will be "filled", but the 10 won't be (since 4 does not divide evenly into 10). To help visualize this idea, imagine that the base of the box is 12x16. This means that a 3x4 "layer" of cubes will fit the base of the box; 12 cubes are in this layer. We can put another "layer" of 12 cubes on top of the first layer, but then the remaining space won't be enough to hold any more cubes.

2 layers of 12 cubes = 24 cubes

Final Answer: D

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phanikpk: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Fri Jun 06, 2014 11:48 pmFollowed by: 1 member

by phanikpk » Tue Jul 15, 2014 1:19 am

Oh thanks rich
I forgot to take care of dimensions of base

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jul 15, 2014 2:30 am

[email protected] wrote:What is the maximum number of 4x4x4 cubes that can fit in a rectangular box measuring 10x12x16 ?

12

18

20

24

30

Follow the colors:
(10 * 12 * 16) / (4 * 4 * 4) = (2.5 * 3 * 4).
Since there can't be 2.5 cubes along the first dimension, the maximum number of cubes that can fit in the box = 2*3*4 = 24.

The correct answer is D.

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by [email protected] » Tue Jul 15, 2014 10:35 am

Hi phanikpk,

To help you stay focused in these types of questions, it often helps to draw pictures (for Geometry questions) or make "tables" of information (for story problems and really detailed questions).

Be mindful of the details - every question on the GMAT was written by a human, to test you on certain concepts, reward you if you can spot patterns and punish you if you make silly mistakes.

GMAT assassins aren't born, they're made,
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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Tue Jul 15, 2014 10:37 am

[email protected] wrote:What is the maximum number of 4x4x4 cubes that can fit in a rectangular box measuring 10x12x16 ?

12

18

20

24

30

Sides of the Bigger box are 10, 12 and 26

Number of Small cubes of Dimension 4 that can occupy the side 10 = [10/4] = 2
Number of Small cubes of Dimension 4 that can occupy the side 12 = [12/4] = 3
Number of Small cubes of Dimension 4 that can occupy the side 16 = [16/4] = 4

Therefore Total Such Small Cubes that can fit into box = 2 x 3 x 4 = 24

Answer: Option D

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unknown13: Senior | Next Rank: 100 Posts; Posts: 31; Joined: Thu Jun 04, 2009 12:01 am; Thanked: 1 times

by unknown13 » Tue Jul 15, 2014 11:25 pm

hi
IMO the answer is D
logic used i the dividing respective dimensions to check the whole number
10/4 = 2.5, 12/4=3, 16/4=4
2.5 cube is not possible so ~2
count of cubes will be 2*3*4 = 24

thanks and regards

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