Cubes- 4GMAT.com

[kanha81]

This question is straight from www.4gmat.com. Can this type of question be asked in actual GMAT exam?

q: 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

What should be the best approach to solve the questions? I could not let my imagination run wild past step 1 ie. finding the volume of the cube.

Any answers/take aways greatly appreciated.

kanha

[relic]

I believe I've seen a similar question on an SAT, so I suppose it's valid for the GMAT.

The volume of the cube is not relevant. Instead, imagine cutting the large cube into the 1cm sided smaller cubes. You'd create a 5 x 5 x 5 matrix of the smaller cubes, or a total of 125 smaller cubes. Now, only the outside surface of the large cube was painted, so only the outer layer of our small cube matrix will have any painted sides. Of course the cubes that make the corners of the large cube will be painted on 3 sides, so those are out. And any small cube that create the edges of the large cube will have 2 sides painted. So the only the landlocked (not on the edge) cubes making up the surface of the large cube will have a single painted side. Each face of the large cube will have 9 of these landlocked cubes. Since there are 6 faces on a cube there will 54 cubes with single sided paint jobs in total.