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When 88 cubes are rearranged to form the solid structure shown in the

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When 88 cubes are rearranged to form the solid structure shown in the  [#permalink]

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New post 24 May 2019, 17:05
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A
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  55% (hard)

Question Stats:

61% (02:22) correct 39% (01:57) wrong based on 28 sessions

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When 88 cubes are rearranged to form the solid structure shown in the diagram below, their total surface area decreases by 384 units. Find the total surface area of the solid structure.

A. 96
B. 128
C. 144
D. 160
E. 176

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Re: When 88 cubes are rearranged to form the solid structure shown in the  [#permalink]

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New post 24 May 2019, 20:22
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nick1816 wrote:
When 88 cubes are rearranged to form the solid structure shown in the diagram below, their total surface area decreases by 384 units. Find the total surface area of the solid structure.

A. 96
B. 128
C. 144
D. 160
E. 176




Here is my approach to the above problem.

Surface area of a cube is 6*(x^2) where x is the length of the cube.

Now,

Surface area of 88 cubes before they form the solid structure = 88 * 6 * x^2= 528* (x^2)


Surface area of the solid structure =

Surface area of each face of solid structure = 16 small cubes with one face exposed (4 hidden are further compensated in the structure that is overlaying)+ 8 side faces of each structure overlaying (more like walls supporting them) = 24 cubes with only one side exposed.

We know total faces of a cube is 6 .So total Surface area of solid structure = 24* 6* x^2 = 144 *x^2


Now from question

When 88 cubes are rearranged to form the solid structure shown in the diagram below, their total surface area decreases by 384 units.

Implies

528* (x^2) - 144 *x^2= 384

384*(x^2) =384

x = 1


Therefore total surface area of solid structure = 144 *x^2 = 144

So I guess C should be the option.



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Re: When 88 cubes are rearranged to form the solid structure shown in the  [#permalink]

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New post 05 Aug 2019, 17:47
gmatbusters chetan2u, VeritasKarishma,

Please review my approach

SA of cube = \(6 s^2\)

According to the given statement in the question:
384 = ( 6 x 88 \(s^2\) ) - x (x being the required SA we have to find)

x = 528 \(s^2\) - 384
After this I just assumed s=1 and hence 528 - 384 = 144 (answer)

Is the right approach in an actual test scenario? If not what method should one use which can be successful always
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Re: When 88 cubes are rearranged to form the solid structure shown in the  [#permalink]

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New post 06 Aug 2019, 00:29
DarkHorse2019 wrote:
gmatbusters chetan2u, VeritasKarishma,

Please review my approach

SA of cube = \(6 s^2\)

According to the given statement in the question:
384 = ( 6 x 88 \(s^2\) ) - x (x being the required SA we have to find)

x = 528 \(s^2\) - 384
After this I just assumed s=1 and hence 528 - 384 = 144 (answer)

Is the right approach in an actual test scenario? If not what method should one use which can be successful always


You can't assume that s = 1. You have to find it as done by prabsahi above. What if the length of each side of the small cube is 2 units?
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Re: When 88 cubes are rearranged to form the solid structure shown in the   [#permalink] 06 Aug 2019, 00:29
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