Take an easy cube side for example 2.

Let's focus on one rectangle, it is now 2*2*1
The total surface is 2*2 + 2*2 + 1*2 + 1*2 + 1*2 + 1*2=16
The surface which is not painted is 2*2=4
(Draw a cube)
So 4/16=1/4

I agree with pepe.....Ans is 25%...
Did wid the same method

Picking numbers is a great way to solve.

We could also reason it out:

If we cut the cube down the middle, our new shape will also have 6 sides, 5 of which will be red (only the exposed middle will be white).

Two of the 6 sides will be full-sized (the white side and the side opposite) and 4 will be half-sized (the 4 sides "ringing" the white side). Let's call the area of a full side x and the area of a half side .5x; so, the entire surface area will be:

2(x) + 4(.5x) = 2x + 2x = 4x.

The white side has area x, so the proportion of the shape that's white is x/4x = 1/4.

Can you explain this more to me. I guess I am having a problem envisioning it. I understand thet 2 of teh sides will be full sized but DONT understand other 4 sides.

Two of the 6 sides will be full-sized (the white side and the side opposite) and 4 will be half-sized (the 4 sides "ringing" the white side). Let's call the area of a full side x and the area of a half side .5x; so, the entire surface area will be:

pre-gmat wrote:Can you explain this more to me. I guess I am having a problem envisioning it. I understand thet 2 of teh sides will be full sized but DONT understand other 4 sides.

Two of the 6 sides will be full-sized (the white side and the side opposite) and 4 will be half-sized (the 4 sides "ringing" the white side). Let's call the area of a full side x and the area of a half side .5x; so, the entire surface area will be:

We're making our cut parallel to the sides to create two rectangular boxes with equal volume - in other words, we're cutting the cube in half.

Let's simplify to 2 dimensions. If you cut a square with sides of 1 to create two equally sized rectangles, each rectangle will have dimensions of 1 * 1/2. Now think of that square as the top face of a cube, and you're cutting all the way through instead of just the surface. The top of the shape you've created has dimensions of 1 * 1/2, as do the bottom and 2 of the sides. The surface along which the knife traveled is still a full square, as is the side opposite that one.

Perfect I got it now:)

I guess I was combining the cut sides of the rectangle.

Thnx a ton:)

Thanks guys,

But still not getting it how is the white side and the side opposite is full sized, and the other 4 are half sized? Please Explain.

Try taking a cube of Tofu and cut it parallel to sides. You will see that the length of 2 sides is intact and the 4 are cut in Halves)

Stuart's logic is excellent in explaining this. Try reading it 2-3 times.