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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 5:

This is a super hard question, because it involves a lot of calculation. Basically, we have to add all columns of cubes on the right-most layer of the larger cube. Each column is an AP with first term the number on the bottom layer, and common difference 64.

Sum=(2a+(n−1)d)\\frac{n}{2}\\)

Sum for First Column:Sum=(2×8+(8−1)64)×4=1856
Sum for Second Column:Sum=(2×16+(8−1)64)×4=1920:
Sum for Third Column:Sum=(2×24+(8−1)64)×4=1984:
We can quickly see the pattern (that each column exceeds the previous by 64).
Sum of all columns: Sum=(2×1856+(8−1)64)×4=16640.

The question is "Find the sum of all the numbers on the cubes on this surface."

Hence, the answer is "16640".