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rectangular carton

by gmat009 » Wed Oct 01, 2008 10:05 pm
The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3 : 2 : 2. In terms of x, which of the following equals the height of the carton, in feet?
A. Cube root x
B. Cube root (2x/3)
C. Cube root (3x/2)
D. 2/3 (Cube root x)
E. 3/2(Cube root x)
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by Mani_mba » Wed Oct 01, 2008 10:22 pm
L:w:H = 3:2:2

12K^3 = x
K = cube root(x/12)

Height = 2K = 2 * cube root(x/12)
= 2 * cube root(x) / cube root (2^2 * 3)
= 2 ^ (1/3) * cube root(x) / cube root(3)
= cube root (2x/3)

Hence B.
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by gmat009 » Wed Oct 01, 2008 10:30 pm
Mani_mba wrote:L:w:H = 3:2:2

12K^3 = x
K = cube root(x/12)

Height = 2K = 2 * cube root(x/12)
= 2 * cube root(x) / cube root (2^2 * 3)
= 2 ^ (1/3) * cube root(x) / cube root(3)
= cube root (2x/3)

Hence B.
Ans is right but I am not clear with your method, specially 1st step.

12K^3 = x ----------- How u got this.
K = cube root(x/12)
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by Mani_mba » Wed Oct 01, 2008 10:41 pm
As L,W and H are in the ratio of 3:2:2,

L can be written as 3k
W can be written as 2k
H can be written as 2k

Vol = LWH
= 3K * 2k * 2k
= 12 * k^3

HTH
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by gmat009 » Wed Oct 01, 2008 10:54 pm
Mani_mba wrote:As L,W and H are in the ratio of 3:2:2,

L can be written as 3k
W can be written as 2k
H can be written as 2k

Vol = LWH
= 3K * 2k * 2k
= 12 * k^3

HTH
Got it..........
Thanks......
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