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A large solid cube is assembled by gluing together identical

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A large solid cube is assembled by gluing together identical [#permalink]

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New post 17 Apr 2013, 23:01
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A large solid cube is assembled by gluing together identical unpainted small cubic blocks. All six faces of the large cube are then painted red. If exactly 27 of the small cubic blocks that make up the large cube have no red paint on them, how many small cubic blocks make up the larger cube?

A 120
B 125
C 135
D 145
E 150

[Reveal] Spoiler:
OA 125
[Reveal] Spoiler: OA

Last edited by Zarrolou on 18 Apr 2013, 00:50, edited 1 time in total.
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Re: A large solid cube is assembled by gluing together identical [#permalink]

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New post 17 Apr 2013, 23:09
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The inner cube has an area of 27 so has a side of 3.

To obtain the larger cube we have to sum a cube to each and of a side \(1+3+1=5\) So the area of the larger cube is \(5^3=125\)

Similar question: 64-small-identical-cubes-are-used-to-form-a-large-cube-151009.html#p1212964
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Re: A large solid cube is assembled by gluing together identical [#permalink]

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New post 18 Apr 2013, 00:41
Thankyou for taking the time to answer, but I dont understand. Why is the side 3?
And why have you added 1+1+3?
A 120 B125 C 135 D145 E150
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Re: A large solid cube is assembled by gluing together identical [#permalink]

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usre123 wrote:
Thankyou for taking the time to answer, but I dont understand. Why is the side 3?
And why have you added 1+1+3?
Also, as I explained in the pm, we got a handout of these in our gmat class, and the questions just had one single answer. So I dont have the five answer choices.


The inner cube has an area of 27, we know that the area of a coube is \(side^3\) so in this case \(s^3=27\) so \(s=3\)
The inner cube has a side of 3. Good!

Moving on... This is an inner cube, so is contained in a larger cube. The larger cube must contain the inner cube, and this is possible only if the larger cube has at the end of each side one more cube (look at the image: it's in 2D but the concept is the same)
So we add 1 cube to each side 1+3+1=5, the larger cube has a side of 5 => \(area=5^3=125\)

Hope it's clear now, let me know
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Re: A large solid cube is assembled by gluing together identical [#permalink]

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New post 18 Apr 2013, 04:05
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usre123 wrote:
A large solid cube is assembled by gluing together identical unpainted small cubic blocks. All six faces of the large cube are then painted red. If exactly 27 of the small cubic blocks that make up the large cube have no red paint on them, how many small cubic blocks make up the larger cube?

A 120
B 125
C 135
D 145
E 150

[Reveal] Spoiler:
OA 125


This question can be answered without any calculation. The correct answer will have to be of the form \(x^3\), where x is an integer.

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Re: A large solid cube is assembled by gluing together identical [#permalink]

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New post 19 Apr 2013, 20:35
Area of a cube is side squared into 6, for six faces. Here your calculationg the volume by saying side cubed. Just that part i dont get. Why are we calculating volume? Thanks.
Also, youve added one to each side. But we could add any number, such as two etc. And it would change the total blocks...
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Re: A large solid cube is assembled by gluing together identical [#permalink]

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New post 19 Apr 2013, 22:07
usre123 wrote:
Area of a cube is side squared into 6, for six faces. Here your calculationg the volume by saying side cubed. Just that part i dont get. Why are we calculating volume? Thanks.
Also, youve added one to each side. But we could add any number, such as two etc. And it would change the total blocks...


Hi usre123,

We know that the inner cube has an area of 27, to find the side of a cube (with the area) we have to use \(side^3=Area\) and that exactly what we do here. The formula for the area of the cube is not much helpful here...

The second question is a good one, and the answer is in the main question itself. We cannot add more than one cube because EXACTLY 27 cubes are not painted, if we add more than 1 cube, than the number of not painted cubes will be more than 27.

Hope this helps, let me know
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Re: A large solid cube is assembled by gluing together identical [#permalink]

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New post 20 Sep 2013, 07:41
This is a gr8 example of a situation when you are running short of time during the exam.
To make up a cubic block using smaller cubic blocks we would always need \(a^3\) no of blocks.

And 125 is the only option which is a perfect cube of an integer i.e. 125 = \((5)^3\)
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Re: A large solid cube is assembled by gluing together identical [#permalink]

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New post 20 Sep 2013, 10:33
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usre123 wrote:
A large solid cube is assembled by gluing together identical unpainted small cubic blocks. All six faces of the large cube are then painted red. If exactly 27 of the small cubic blocks that make up the large cube have no red paint on them, how many small cubic blocks make up the larger cube?

A 120
B 125
C 135
D 145
E 150

[Reveal] Spoiler:
OA 125


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Re: A large solid cube is assembled by gluing together identical [#permalink]

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Re: A large solid cube is assembled by gluing together identical   [#permalink] 20 Apr 2016, 02:43
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