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20 Jul 2015, 13:01
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
65% (02:01) correct
35%
(02:15)
wrong
based on 78
sessions
History
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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)
A) (x/12)^(1/3)
B) (x/6)^(1/3)
C) (x/4)^(1/3)
D) (2x/3)^(1/3)
E) (x)^(1/3)
ENGRTOMBA2018
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,319
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
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20 Jul 2015, 13:18
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\(\)
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.
Mascarfi
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.
21 Jul 2015, 02:57
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Mascarfi
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
