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# A cube and a rectangular solid are equal in volume. If the lengths of

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Math Expert
Joined: 02 Sep 2009
Posts: 52412
A cube and a rectangular solid are equal in volume. If the lengths of  [#permalink]

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08 Jan 2019, 04:14
00:00

Difficulty:

25% (medium)

Question Stats:

88% (00:53) correct 13% (01:19) wrong based on 32 sessions

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A cube and a rectangular solid are equal in volume. If the lengths of the edges of the rectangular solid are 4, 8, and 16, what is the length of an edge of the cube?

A. 4
B. 8
C. 12
D. 16
E. 64

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Location: India
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Re: A cube and a rectangular solid are equal in volume. If the lengths of  [#permalink]

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08 Jan 2019, 04:25
Bunuel wrote:
A cube and a rectangular solid are equal in volume. If the lengths of the edges of the rectangular solid are 4, 8, and 16, what is the length of an edge of the cube?

A. 4
B. 8
C. 12
D. 16
E. 64

vol= 4*8*16 = 512
side of cube = (512)^1/3
= 8 IMO B
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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8806
Location: Pune, India
Re: A cube and a rectangular solid are equal in volume. If the lengths of  [#permalink]

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08 Jan 2019, 05:00
1
Bunuel wrote:
A cube and a rectangular solid are equal in volume. If the lengths of the edges of the rectangular solid are 4, 8, and 16, what is the length of an edge of the cube?

A. 4
B. 8
C. 12
D. 16
E. 64

Volume of a cube = Side^3
Volume of a rectangular solid = Length*Breadth*Height = 4*8*16 = 2^9

Given $$Side^3 = 2^9 = (2^3)^3 = 8^3$$

$$Side = 8$$
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Karishma
Veritas Prep GMAT Instructor

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Joined: 15 Feb 2018
Posts: 204
Re: A cube and a rectangular solid are equal in volume. If the lengths of  [#permalink]

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17 Jan 2019, 23:25
Geometric mean.
3√($$2^2·2^3·2^4$$)=$$2^{9/3}$$=$$2^3$$=8
Re: A cube and a rectangular solid are equal in volume. If the lengths of &nbs [#permalink] 17 Jan 2019, 23:25
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