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# One dimension of a cube is increased by 1, another is decreased by 1,

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Math Expert
Joined: 02 Sep 2009
Posts: 58428
One dimension of a cube is increased by 1, another is decreased by 1,  [#permalink]

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28 Mar 2019, 05:57
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Difficulty:

15% (low)

Question Stats:

85% (02:00) correct 15% (01:14) wrong based on 34 sessions

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One dimension of a cube is increased by 1, another is decreased by 1, and the third is left unchanged. The volume of the new rectangular solid is 5 less than that of the cube. What was the volume of the cube?

(A) 8
(B) 27
(C) 64
(D) 125
(E) 216

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Joined: 13 Feb 2018
Posts: 450
GMAT 1: 640 Q48 V28
Re: One dimension of a cube is increased by 1, another is decreased by 1,  [#permalink]

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28 Mar 2019, 09:06
Let a be the side of the cube. The volume of the cube $$a^3$$
After adjustment the new figure has the volume: (a-1)(a+1)(a)=$$a^3$$-a

According to the stem: $$a^3$$-($$a^3$$-a)=5
a=5

The volume of the initial cube is 125

Imo
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Re: One dimension of a cube is increased by 1, another is decreased by 1,  [#permalink]

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31 Mar 2019, 11:47
Bunuel wrote:
One dimension of a cube is increased by 1, another is decreased by 1, and the third is left unchanged. The volume of the new rectangular solid is 5 less than that of the cube. What was the volume of the cube?

(A) 8
(B) 27
(C) 64
(D) 125
(E) 216

We can create the equation:

n^3 = (n + 1)(n - 1)n + 5

n^3 = (n^2 - 1)n + 5

n^3 = n^3 - n + 5

n = 5

So the volume of the original cube was 5^3 = 125.

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Re: One dimension of a cube is increased by 1, another is decreased by 1,   [#permalink] 31 Mar 2019, 11:47
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