<p>tCB Online course, practice test 1.</p>
<p>A large solid cube is assembled by gluing together identical unpainted small cubic
blocks. All six faces of the large cube are then painted red. If exactly 27 of the small
cubic blocks that make up the large cube have no red paint on them, how many small
cubic blocks make up the large cube?</p>
<p>Answer is 125. Can anyone give me a method for this?</p>
<p>if 27 cubes dont have paint, that means they are on the inside of the large cube
this means that the 27 cubes make a smalller cube inside the larger cube with side length of the 3 cubes because 3^3 = 27. Because the cubes around those inner cubes have paint and create a larger cube, the larger cube has a length of 5 cubes. This means 5^3 cubes make up the entire thing = 125 cubes</p>
<p>I can see the logic behind the explanation, but how did you conceive of the method? I spent 5 minutes on this one question alone trying to figure this out, and I usually get 800’s in math.</p>
<p>The way I solved this one was using intuition…I think you are trying too hard to use conventional methods. Sometimes, the questions need some intuitive thinking to solve.</p>
<p>Try to visualize the cube.</p>
<p>The smaller cubes that have red paint on them constitute the outer shell > so, imagine a cube within a cube. Forget about the red bits and concentrate on the inner cube. It’s made up of 27 small cubes > pretty straight-forward calculation here, each side is 3 cubes long. NOW imagine the red layer around it (not entirely red, technically, but this is irrelevant). Add one small cube to each side of the one you already know about–the outer layer–and you get 5.</p>
<p>I don’t know how else to explain it, it’s just a very easy problem if you can imagine it clearly. It’s supposed to test your three-dimensional thinking.</p>