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A large solid cube is assembled by gluing together...

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by BTGmoderatorLU » Sun Jan 07, 2018 7:44 am
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 not red paint on them, how many small cubic blocks make up the larger cube?

A. 120
B. 125
C. 135
D. 145
E. 150

The OA is B.

I'm confused with this PS question. Experts, any suggestion about the solution? Thanks in advance.
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by EconomistGMATTutor » Tue Jan 09, 2018 3:10 am
Hello LUANDATO.

Let's see. We have that 27 of the small cubic blocks have not red paint on them. It implies that they were under the last layer of cubic blocks. So, we have that a cube of 3x3x3 was inside of the larger cube.

Therefore, the dimensions of the larger cube were 5x5x5. It implies that the larger cube was formed using 125 small cubic blocks.

This is why the correct answer is the option [spoiler]B=125[/spoiler].

I hope this explanation may help you.

Feel free to ask me again if you have a doubt.

Regards.
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by EconomistGMATTutor » Tue Jan 09, 2018 3:10 am
Hello LUANDATO.

Let's see. We have that 27 of the small cubic blocks have not red paint on them. It implies that they were under the last layer of cubic blocks. So, we have that a cube of 3x3x3 was inside of the larger cube.

Therefore, the dimensions of the larger cube were 5x5x5. It implies that the larger cube was formed using 125 small cubic blocks.

This is why the correct answer is the option [spoiler]B=125[/spoiler].

I hope this explanation may help you.

Feel free to ask me again if you have a doubt.

Regards.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

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