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# What is the length of a rectangular solid of height 6 that

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Joined: 15 Dec 2003
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What is the length of a rectangular solid of height 6 that [#permalink]  26 Aug 2004, 09:09
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What is the length of a rectangular solid of height 6 that is twice as long as it is wide, if its volume is the same as that of a cube with total surface area of 864 square inches?
A) 12
B) 14
C) 24
D) 30
E) 36
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Paul

Joined: 31 Dec 1969
Location: India
Concentration: Strategy, Human Resources
GMAT 1: 710 Q49 V0
GMAT 2: 740 Q40 V50
GMAT 3: 700 Q48 V38
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GPA: 3.31
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Kudos [?]: 93 [0], given: 88341

volume of rectangle-Lx2Lx6. Lenght of a side of a square is 6xA^2=864 or A^2=144 so A is 12. The volume of the cube is 1728. Then 12xL^2=12^3 or L=12 so the lenght of the rectangle is 24.
Senior Manager
Joined: 07 Oct 2003
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Location: Manhattan
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Kudos [?]: 9 [0], given: 0

Anonymous wrote:
volume of rectangle-Lx2Lx6. Lenght of a side of a square is 6xA^2=864 or A^2=144 so A is 12. The volume of the cube is 1728. Then 12xL^2=12^3 or L=12 so the lenght of the rectangle is 24.

good work, the only thing is that a cube is not necessarily considered a square. A rectangular solid in which all edges are of equal length is a cube. However, it doesn't have to have 90 degree angles and thus doesn't have to be a square. Great solution nevertheless
GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4309
Followers: 29

Kudos [?]: 235 [0], given: 0

OA is 24
Just thought 12 could have been a trap answer for someone not paying carefull attention to the "length" instead of the "width"
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Best Regards,

Paul

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