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.
Unable to proceed after calculating x. Help.
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Let L=3, W=2 and H=2.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
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, can you please explain this? How did we take "2 inside the cube root"?Anindya Madhudor wrote:Take 2 inside the cube root. Then,
H = cube root(8x/12) = cube root(2x/3)
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.
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.
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
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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Hi All,
We’re told that the interior of a rectangular carton holds a volume of X cubic feet and the ratio of Length : Width : Height = 3 : 2 : 2. We’re asked which of the 5 answers is equal to the HEIGHT in feet. While the answers to this question “look scary”, we can answer this question rather handily by TESTing VALUES.
IF… Length = 3, Width = 2 and Height = 2, then the Volume = X = (3)(2)(2) = 12 cubic feet. This means that we’re looking for an answer that equals 2 when X = 12
Since the cube-root of 8 = 2 and the cube-root of 27 = 3, we know that the cube-root of 12 will NOT be an integer (and will likely be an ugly decimal). Since we’re looking for an answer that equals 2 (re: a nice, round integer), we can quickly eliminate several answers because they will clearly NOT be integers. Eliminate Answers A, D and E
Between the two answers that remain, since both involve cube-roots and we need the final result to equal 2, we’re looking for a total under the radical that equals 8. There’s only one answer that matches…
Final Answer: B
GMAT Assassins aren’t born, they’re made,
Rich
We’re told that the interior of a rectangular carton holds a volume of X cubic feet and the ratio of Length : Width : Height = 3 : 2 : 2. We’re asked which of the 5 answers is equal to the HEIGHT in feet. While the answers to this question “look scary”, we can answer this question rather handily by TESTing VALUES.
IF… Length = 3, Width = 2 and Height = 2, then the Volume = X = (3)(2)(2) = 12 cubic feet. This means that we’re looking for an answer that equals 2 when X = 12
Since the cube-root of 8 = 2 and the cube-root of 27 = 3, we know that the cube-root of 12 will NOT be an integer (and will likely be an ugly decimal). Since we’re looking for an answer that equals 2 (re: a nice, round integer), we can quickly eliminate several answers because they will clearly NOT be integers. Eliminate Answers A, D and E
Between the two answers that remain, since both involve cube-roots and we need the final result to equal 2, we’re looking for a total under the radical that equals 8. There’s only one answer that matches…
Final Answer: B
GMAT Assassins aren’t born, they’re made,
Rich