Six identical solid metal cubes are to be polished with gold on all su

Question

Six identical solid metal cubes are to be polished with gold on all surfaces before being displayed in a showroom. To reduce the amount of gold needed for polishing, the showroom managers are contemplating welding the six cubes together, thereby forming a rectangular solid before polishing. They are contemplating two ways of doing so - by joining all six cubes together (1 × 6 row) and forming a long, rectangular solid or by forming a 2 × 3 matrix.

In the table, select the values that, approximately, represent the percentage of gold saved in polishing the solids by joining them in 1 × 6 row and 2 × 3 matrix respectively, compared to the amount of gold needed if the six cubes were to be polished separately. Make only two selections, one in each column.

catinabox · Answer

Let's assume that the side of the cube is of length = x

In the base case, 
Surface area of a cube = 6x^2
Surface area of 6 cubes = 6* 6x^2 = 36x^2

Case 1:
1x6 Matrix
This is a cuboid of length = 6x, breadth =x, and height = x.
Surface area = 2 * x^2 + 4 * (6x*x) = 2x^2 + 24x^2
= 26x^2

Savings in area over base case = (36x^2 - 26x^2 )/36x^2 = 10/36 = 28%

Case 2:
2x3 Matrix
This is a cuboid of length =3x, breadth = 2x and height = 2x
Surface area = 2 * ( 2x*3x + x*2x + x*3x)
= 22x^2

Savings in area over base case = (36x^2 - 22x^2)/36^2 = 14/36 = 39%

Vidds0214 · Answer

Does this partially come under geometry?

Bunuel · Answer

Yes. However, while specific geometry knowledge is not tested on GMAT Focus, not everything involving shapes, volumes, or areas requires specialized geometry knowledge. The area of a square or rectangle, the volume of a cube or rectangular solid, and the Pythagorean theorem are not considered specific geometry knowledge by the GMAT and can still be tested. Moreover, a question can involve shapes but test another area, such as combinations or other topics. There are several  questions involving these concepts in the GMAT Prep Focus mocks .

rohanbullseyeaim · Answer

case 2 2 (lb+bh+hl) = should it not be 2(2.3+2.2+2.3_) = 2(6+4+6) = 32 ? how is it 22

SatvikVedala · Answer

Hi  catinabox

In case 2 the breadth is misrepresented as 2x (against x)

However the calculation considers x

-it's Satvik-
I was here, I was solving & I was learning

Robo_123 · Answer

Is this question relevant for the focus edition? Are we supposed to memorise the formulae?

Bunuel · Answer

I believe your doubt is addressed here: https://gmatclub.com/forum/six-identica ... l#p3450034 Let me know if any questions.

kdipayan · Answer

The dimensions of 2x3 cube matrix should be 3x, 2x and x. Please check.

TIA

Adit_ · Answer

IMO no need of any formula,
take each side of cube as 1 unit, total area of each is 6 therefore 6 cubes will be 36 unit^2
Now when u combine it to a cuboid, notice the number of sides thats not used,
1st cube ->1
2nd cube -> 2
the middle cubes all receive 2 in this case and the last cube is again 1, totally 10 sides not used as compared to before so 10/36*100=28%

For second case,
the middle ones have 3 sides unused this time and the corner ones have each 2 unused
therefore total=2+3+2+2+3+2=14

Percent=14/36*100=39%

1 x 6 row	2 x 3 matrix	Percentage saving
		20%
		28%
		33%
		39%
		42%

Six identical solid metal cubes are to be polished with gold on all su

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