MGMAT

I would probably just find what cube I have remaining, and subtract the new number of cubes from the 1000.
you start with 10*10*10.

Remove a top layer from the front, so the cube is only 9 cubes "wide": 10*9*10
shave a layer from the top face ("above it"), so the cube is only 9 cubes "high": 10*9*9
Now shave a layer from the side ("to the right of the first") so the cube is only 9 cubes "long": 9*9*9

Every time you shave a layer, you reduce 1 from one dimension, leaving the others as they are. Thus, if we repeat the process for all three dimensions (even in reverse order), we get 8*8*8. If we take another layer from the first face, we take another 1 from the width to get 8*7*8
How we call the dimensions "length, width height" does not really matter: the dynamic is the same, and the result will be two 8s and a 7.

Now the question asked how many have been removed, so the final answer is {original number - new number} = 10*10*10 - 8*8*7 = 1000 - 64*7 = 1000 - 448 = 552. Answer should be B.

Great!! thank Geva!

We can answer this by keeping track of how many cubes are lopped off of each side as the cube is trimmed (10 x 10 + 10 x 9 + 9 x 9 + ...), but this approach is tedious and error prone. A more efficient method is to determine the final dimensions of the trimmed cube, then find the difference between the dimensions of the trimmed and original cubes.

Let's call the first face A, second face B, and third face C. By the end of the operation, we will have removed 2 layers each from faces B and C, and 3 layers from face A. So B now is 8 cubes long, C is 8 cubes long, and A is 7 cubes long. The resulting solid has dimensions 8 x 8 x 7 cubes or 448 cubes. We began with 1000 cubes, so 1000 - 448 = 552. Thus, 552 cubes have been removed.

The correct answer is B