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

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Manager
Joined: 08 May 2015
Posts: 97
GMAT 1: 630 Q39 V38
GMAT 2: 670 Q44 V38
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A rectangular box of volume x has width, depth and height in the ratio  [#permalink]

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20 Jul 2015, 12:01
3
00:00

Difficulty:

35% (medium)

Question Stats:

69% (02:11) correct 31% (02:15) wrong based on 80 sessions

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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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Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
A rectangular box of volume x has width, depth and height in the ratio  [#permalink]

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20 Jul 2015, 12:18
2

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]

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21 Jul 2015, 01:57
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

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Re: A rectangular box of volume x has width, depth and height in the ratio  [#permalink]

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21 Jul 2015, 13:59
1
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?
CEO
Joined: 20 Mar 2014
Posts: 2633
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: A rectangular box of volume x has width, depth and height in the ratio  [#permalink]

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21 Jul 2015, 15:05
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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Posts: 9082
Re: A rectangular box of volume x has width, depth and height in the ratio  [#permalink]

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12 Nov 2017, 18:18
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# A rectangular box of volume x has width, depth and height in the ratio

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