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

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VP
Joined: 19 Oct 2018
Posts: 1158
Location: India
When 88 cubes are rearranged to form the solid structure shown in the  [#permalink]

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24 May 2019, 17:05
1
00:00

Difficulty:

65% (hard)

Question Stats:

59% (02:22) correct 41% (02:08) wrong based on 29 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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Senior Manager
Joined: 09 Jun 2014
Posts: 353
Location: India
Concentration: General Management, Operations
Re: When 88 cubes are rearranged to form the solid structure shown in the  [#permalink]

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24 May 2019, 20:22
2
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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Manager
Joined: 29 Dec 2018
Posts: 82
Location: India
WE: Marketing (Real Estate)
Re: When 88 cubes are rearranged to form the solid structure shown in the  [#permalink]

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05 Aug 2019, 17:47

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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Keep your eyes on the prize: 750
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9855
Location: Pune, India
Re: When 88 cubes are rearranged to form the solid structure shown in the  [#permalink]

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06 Aug 2019, 00:29
DarkHorse2019 wrote:

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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Karishma
Veritas Prep GMAT Instructor

Re: When 88 cubes are rearranged to form the solid structure shown in the   [#permalink] 06 Aug 2019, 00:29
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