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HCF and LCM Factors Remainders Factorials Digits Ratios,Mixtures;Averages Percents; Profits; SICI Speed & Time; Races Logarithms and Exponents Pipes,Cisterns; Work,Time Set Theory Geometry Coordinate Geometry Mensuration Linear & Quadratic Equations Functions Inequalities Polynomials Progressions Permutation Probability
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Explanatory Answer

Method of solving this Question on Logical Reasoning for CAT:

General Solution:

The first layer of the cube looks like this:



We notice that each of the cubes in the second layer will be 64 + n, where n is the small cube directly below the cube in question. Each of the cubes in the third layer will be 64 x 2 + n, and so on.

In general, to find the number on a particular cube 'P' on the k'th layer, we can use the formula P = (k - 1)x64 + n, where n is the number on the bottom-most cube below P. With this general idea, we can solve the whole puzzle.

Solution for Question 2:

The body diagonal that has the cube numbered 1 starts in the bottom-left-front corner and extends all the way to the top-right-back corner. This cube will have the number P=(8−1)×64+64=512

Basically this is the last cube that is placed.

The question is "Find the number on the small cube at the other end of the body diagonal that has the small cube numbered 1."

Hence, the answer is "512".