There is a big cube of dimension 110 * 154 * 385 made up of smaller 1 * 1 * 1 dimension cubes. A body (main) diagonal is drawn. How many smaller 1 * 1 * 1 cubes will it cut?
Above answer is brilliant! Another way to approach this kind of question is: first take HCF to shrink the big cube into the smallest one with same ratio on 3 dimensions. Usually the smallest cub is manageable; then take the shadow of body (main) diagonal on each of 3 faces. It will reduce to standard # of squares cut by diagonal on each rectangle; then mark the square which got crossed on 3 faces. It will help figure out # of cubs to be crossed. It takes more time this way if you dcan't remember the formula above
Since there has not been any response as of now, here is my solution without a lot of explanation.
For this question, the answer must be: (HCF(x,y,z)) * (1 + (a-1) + (b-1) + (c-1) - (HCF(a,b) - 1) - (HCF(a,c) - 1) - (HCF(b,c) - 1))
where a = x/(HCF(x,y,z) and so on.
11 * (1+9+13+34-1-4-6) = 506