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Rectangular solid

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Rectangular solid

by crackgmat007 » Tue May 05, 2009 9:36 am
D. 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 of x
B. cube root of (2x/3)
C. cube root of (3x/2)
D. 2/3 (cube root of x)
E. 3/2 (cube root of x)

OA - B
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Re: Rectangular solid

by Stuart@KaplanGMAT » Tue May 05, 2009 11:42 am
crackgmat007 wrote:D. 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 of x
B. cube root of (2x/3)
C. cube root of (3x/2)
D. 2/3 (cube root of x)
E. 3/2 (cube root of x)

OA - B
Let's pick numbers (sticking to our ratio):

L = 3
W = 2
H = 2

Vol = x = 3*2*2 = 12

Plugging x=12 into our choices, looking for H=2:

a) cuberoot12 = weird number... wrong
b) cuberoot(24/3) = cuberoot8 = 2.. ding!
c) cuberoot(36/2) = cuberoot18... wrong
d) 2/3(cuberoot12) = weird number.. wrong
e) 3/2(cuberoot12) = weird number.. wrong

only (b) works: choose (b)
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Re: Rectangular solid

by dtweah » Tue May 05, 2009 12:20 pm
crackgmat007 wrote:D. 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 of x
B. cube root of (2x/3)
C. cube root of (3x/2)
D. 2/3 (cube root of x)
E. 3/2 (cube root of x)

OA - B
Find common ratio C.
3:2:2
X=LWH
X=(3c)(2c)(2c)=12c^3

C=(X/12)^1/3

H= 2c= 2(X/12)^1/3

H= 2(2X/2^3 x 3)^1/3 ( rationalize denominator)

H=2 ( (2X/3)^1/3) *1/2

H=(2X/3)^1/3
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