Help with one more GMAT problem solving question

yeah, this one is definitely (c).

you should MEMORIZE the following, and PUT IT ON FLASH CARD(S):

if SIDE of a cube is "s", then:
FACE DIAGONAL of a cube = s√2
MAIN DIAGONAL of the cube = s√3

the face diagonal shouldn't be news - it's just an application of the 45°-45°-90° triangle template - but the main diagonal can be very time-consuming to figure out if you don't memorize it.

flash cards are your friends.

kaf wrote:Hi Lunarpower

if SIDE of a cube is "s", then:
FACE DIAGONAL of a cube = s√2
MAIN DIAGONAL of the cube = s√3

Can you please explain what this means

thanks

take a look at a cube. ideally, you should look at a real, physical model of a cube; if you don't have one available, google around for a VERY good drawing of one.

* the longest diagonal in a cube is called the main diagonal. this goes through the interior of the cube, between opposite vertices. it does NOT go along the sides of the cube.
if you imagine spinning the cube on one of its vertices, as you'd do with a top, then this diagonal will go from the bottom vertex (the one on which the cube is spinning) to the top vertex.
this diagonal has length equal to √3 times the side length of the cube.

* if you just look at ONE of the square faces of the cube, and ignore everything else, then the diagonal of that square face is called a face diagonal.
the length of this diagonal, as can be deduced from a 45-45-90 triangle template, is √2 times the side length of the cube.