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Unable to proceed after calculating x. Help.

This topic has 1 expert reply and 4 member replies

Unable to proceed after calculating x. Help.

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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)

OA: B

3y*2y*2y = x (given)
12y^3 = x
y = cube root(x/12)

Inserting this value of y in 2y...
H = 2y
H = 2*{cube root(x/12)}

I am stuck after this. How do I proceed?

Thanks.

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Senior | Next Rank: 100 Posts Default Avatar
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Take 2 inside the cube root. Then,

H = cube root(8x/12) = cube root(2x/3)

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aman88 wrote:
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)

OA: B
Let L=3, W=2 and H=2.
x = volume = 3*2*2 = 12.
The question stem asks for the value of H=2. This is our target.
Now we plug x=12 into the answers to see which yields our target of 2.
A quick scan of the answer choices reveals that only B works:
(2/3 * x )^(1/3) = (2/3 * 12)^(1/3) = 8^(1/3) = 2.

The correct answer is B.

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Anindya Madhudor wrote:
Take 2 inside the cube root. Then,

H = cube root(8x/12) = cube root(2x/3)
Anindya, can you please explain this? How did we take "2 inside the cube root"?

Thanks.

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2 is equal to cube root of 8.

So, the expression "cube root(8x/12)" is equal to "2 * cube root(x/12)". Think of this in the reverse way. If you are given "cube root(8x/12)", can you write this as "2 * cube root(x/12)"? The answer is yes, you can. So, the opposite is true as well.

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Ver simple approach
Lets assume that the following are the dimensions of the rectangle
Length = 3, Width = 2, Height = 2
These figures comply with the ratio given in the ques.
Vol = 3*2*2 = 12

Cube root of 12 gives decimal value whereas the height that we have taken is an integer.
This eliminates A, D and E
Insert the value in B

cube root((2*12)/3) = 2 and voila B is the option

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