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m23#6

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m23#6 [#permalink] New post 18 Jul 2011, 08:38
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I went through the explanation; however, I am a bit confused with the answer.

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

12
18
20
24
30
The 12x16 floor can be covered with 12 cubes. Another 12 cubes will form the second layer. The height of this construction will be 8; the box won't accommodate any more cubes.

The correct answer is D.


The volume of the n cubes and the box should be same.
so, n*4^3= 10.12.16 =>n = 30.

I dont understand why the base is taken as 12.16 in the explanation. This is not mentioned in the question. We can take the base as 10.16, thus the number of cubes = 10. The height is 12, so, the total number of cubes =30.

Let me know in case I am missing something.
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Re: m23#6 [#permalink] New post 18 Jul 2011, 08:46
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pkmme wrote:
I went through the explanation; however, I am a bit confused with the answer.

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

12
18
20
24
30
The 12x16 floor can be covered with 12 cubes. Another 12 cubes will form the second layer. The height of this construction will be 8; the box won't accommodate any more cubes.

The correct answer is D.


The volume of the n cubes and the box should be same.
so, n*4^3= 10.12.16 =>n = 30.

I dont understand why the base is taken as 12.16 in the explanation. This is not mentioned in the question. We can take the base as 10.16, thus the number of cubes = 10. The height is 12, so, the total number of cubes =30.

Let me know in case I am missing something.


I think we shud have all the dimensions of the rectangle , perfectly divisible by 4. If they are not , then we have to leave some place in the rectangle.

as 10 is not divisible by 4, the next best would be 8.
hence its 8*12*16/4^3 = 24.
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Concentration: Entrepreneurship, Nonprofit
Schools: Stanford GSB - Class of 2015
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Re: M23-06 (Quantitative / Problem solving / Geometry) [#permalink] New post 19 Sep 2012, 13:30
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Imagine a big box with the following measures: H=10 W=12 L=16
Now imagine small boxes with the following measures: H=4 W=4 L=4

We need to figure out how many of the small boxes can fit in the large box.
Grab any two sides of the big box (a rectangle) and identify the number of 4x4 squares that fit that rectangle. For instance, in a 16x10 rectangle we can fit 8 4x4 squares. Then, multiply that number of squares by the side of the big box you didn't use to form the rectangle divided by 4. In this case: 8*(12/4) = 8*3 = 24

Note: Always round down. For instance, if you choose to draw a 16*12 rectangle (that fits 12 4x4 squares), the side measuring 10 when divided by 4 is 2.5, ROUND DOWN, because we want to know how many complete 4x4 boxes we can fit. Using this example, we have that 12*2 = 24

Answer: D
Hope it's clear.
Re: M23-06 (Quantitative / Problem solving / Geometry)   [#permalink] 19 Sep 2012, 13:30
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