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A rectangular box of volume x has width, depth and height in the ratio

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Mascarfi
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A rectangular box of volume x has width, depth and height in the ratio [#permalink] New post   20 Jul 2015, 13:01
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A rectangular box of volume x has width, depth and height in the ratio of 3:2:2 (in this order). What is the height in function of x?

A) (x/12)^(1/3)
B) (x/6)^(1/3)
C) (x/4)^(1/3)
D) (2x/3)^(1/3)
E) (x)^(1/3)
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D
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A rectangular box of volume x has width, depth and height in the ratio [#permalink] New post   20 Jul 2015, 13:18
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Mascarfi wrote:
A rectangular box of volume x has width, depth and height in the ratio of 3:2:2 (in this order). What is the height in function of x?

A) (x/12)^(1/3)
B) (x/6)^(1/3)
C) (x/4)^(1/3)
D) (2x/3)^(1/3)
E) (x)^(1/3)


Method 1:

Use easy numbers as all the options have x as the variable. let x = 12 ( a good number as the ratio is 3:2:2)

Thus x = volume = LWH ---> 12 = 3*2*H ---> H = 2 units.

Now plug in x =12 and see which option give you a value of 2 . Only D gives you a value of 2 and is thus the correct answer.

Method 2:

Alternately, you can use proportions to calculate the height. Let y be the common factor for length, width and height. Thus L=3y, W=2y , H = 2y

Thus, 3y*2y*2y = x ---> \(12y^3 = x\)--->\(y = (x/12)^{1/3}\) and

\(height = 2y= 2 (x/12)^{1/3} = (8x/12)^{1/3} = (2x/3)^{1/3}\) , D is the correct answer.
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A rectangular box of volume x has width, depth and height in the ratio [#permalink] New post   21 Jul 2015, 02:57
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Mascarfi wrote:
A rectangular box of volume x has width, depth and height in the ratio of 3:2:2 (in this order). What is the height in function of x?

A) (x/12)^(1/3)
B) (x/6)^(1/3)
C) (x/4)^(1/3)
D) (2x/3)^(1/3)
E) (x)^(1/3)


Let,width = 3
depth = 2
and height = 2

Then Volume = Width x Depth x Height = 3*2*2 = 12

i.e. x = 12

i.e. The correct Option should result in 2 on substituting the value of x=12

Cheking Options @x=12

A) (x/12)^(1/3) = (12/12)^(1/3) = 1 INCORRECT ANSWER
B) (x/6)^(1/3) = (12/6)^(1/3) = 2^(1/3) INCORRECT ANSWER
C) (x/4)^(1/3) = (12/4)^(1/3) = 3^(1/3) INCORRECT ANSWER
D) (2x/3)^(1/3) = (2*12/3)^(1/3) = 8^(1/3) = 2 CORRECT ANSWER
E) (x)^(1/3) = (12)^(1/3) INCORRECT ANSWER

Answer: Option D
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Re: A rectangular box of volume x has width, depth and height in the ratio [#permalink] New post   21 Jul 2015, 14:59
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Engr2012 wrote:
\(\)
Mascarfi wrote:
A rectangular box of volume x has width, depth and height in the ratio of 3:2:2 (in this order). What is the height in function of x?

A) (x/12)^(1/3)
B) (x/6)^(1/3)
C) (x/4)^(1/3)
D) (2x/3)^(1/3)
E) (x)^(1/3)


Method 1:

Use easy numbers as all the options have x as the variable. let x = 12 ( a good number as the ratio is 3:2:2)

Thus x = volume = LWH ---> 12 = 3*2*H ---> H = 2 units.

Now plug in x =2 and see which option give you a value of 2 . Only D gives you a value of 2 and is thus the correct answer.

Method 2:

Alternately, you can use proportions to calculate the height. Let y be the common factor for length, width and height. Thus L=3y, W=2y , H = 2y

Thus, 3y*2y*2y = x ---> \(12y^3 = x\)--->\(y = (x/12)^{1/3}\) and

\(height = 2y= 2 (x/12)^{1/3} = (8x/12)^{1/3} = (2x/3)^{1/3}\) , D is the correct answer.



Hello,

Should that be x=12 and not the 2 from the height?
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Re: A rectangular box of volume x has width, depth and height in the ratio [#permalink] New post   21 Jul 2015, 16:05
xLUCAJx wrote:
Engr2012 wrote:
\(\)
Mascarfi wrote:
A rectangular box of volume x has width, depth and height in the ratio of 3:2:2 (in this order). What is the height in function of x?

A) (x/12)^(1/3)
B) (x/6)^(1/3)
C) (x/4)^(1/3)
D) (2x/3)^(1/3)
E) (x)^(1/3)


Method 1:

Use easy numbers as all the options have x as the variable. let x = 12 ( a good number as the ratio is 3:2:2)

Thus x = volume = LWH ---> 12 = 3*2*H ---> H = 2 units.

Now plug in x =2 and see which option give you a value of 2 . Only D gives you a value of 2 and is thus the correct answer.

Method 2:

Alternately, you can use proportions to calculate the height. Let y be the common factor for length, width and height. Thus L=3y, W=2y , H = 2y

Thus, 3y*2y*2y = x ---> \(12y^3 = x\)--->\(y = (x/12)^{1/3}\) and

\(height = 2y= 2 (x/12)^{1/3} = (8x/12)^{1/3} = (2x/3)^{1/3}\) , D is the correct answer.



Hello,

Should that be x=12 and not the 2 from the height?


Yes, it should be x =12. Thanks, I have edited the typo.
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Re: A rectangular box of volume x has width, depth and height in the ratio [#permalink] New post   12 Nov 2017, 19:18
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Re: A rectangular box of volume x has width, depth and height in the ratio [#permalink]
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