A cube of side 5cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?

A. 9
B. 61
C. 98
D. 54
E. 64

I think the quickest way is to imagine in your mind 1 side of the cube. Understand that the border cubes will have more than one side painted, so the ones with only one side are the ones in the middle, in this case 3x3=9. Then multiply that by 6 sides. If you will make a diagram, make only one side and then multiply by 6. Don't waste the little precious time that you have.
See the picture below to understand it better. The green squares have adjacent surfaces painted. Only the blue ones have 1 side only painted.

9 such cubes for each of the 6 surfaces = 9 * 6 = 54 cubes. (D)

are you sure it's a 5 cubic centimeter cube or is it a 5 cubic metre cube?? there should be five 1 cubic centimeter cubes when a 5 cubic centimeter cube is cut up

My assumption was exactly the same. I didn't think that a cube of side 5^(1/3) cm being divided into 1 cubic centimeter cubes makes sense. So, I assumed that each of the sides of the cube was 5 cm (a 5 cm cube as opposed to 5 cubic centimeter).

A cube of side 5cm is painted on all of its sides. If it is sliced into 1 cubic cm cubes, how many 1 cubic cm cubes will have exactly one of their sides painted?

A. 9
B. 61
C. 98
D. 54
E. 64

all the boundary cubes will have more than one face painted. only the center ones on each side of the larger cube, will have paint on just one side.

if we observer one face, there are 9 such cubes which have only one face painted.

so this times 6 faces we will have 9*6 = 54 such small cubes .

Answer is D.

Hi.. is there any formula to calculate total number of cubes after division.
Let say a 6cm cube is divided into 2cm cubes ?

For those who have a problem in visualising they can atleast come to a conlusion that such cubes will be present on all the six sides. Now, whatever be this number(9 in this case), the answer will be a multiple of 6. Thus, just choose an option which is a multiple of 6.
However, GMAT can give 2 options where in more than 1 option is a multiple of 6. In this question, luckily we have only one such option.

D.
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Not Bunuel, but lets try..

Refer diagram below; just imagine one side of the cube

It will have 5 * 5 = 25 squares of 1 units

The border (the corner squares) will always be 2 side painted, so remaining are the pink shaded squares

There calculation per side = (5-2) * (5-2) = 3*3 = 9
(Two rows & two Columns are to be subtracted)

Total 6 sides = 9*6 = 54

Answer = 54