56. In a certain code if 64 is written as 343 and 216 is written as 729, then how is 512 written in that code?

1. A. 1000
2. B. 1331
3. C. 1728
4. D. 2197

Answer: B

Explanation

Let’s analyze the given coding pattern:
* 64 is coded as 343.
We know 64 = 4³.
We know 343 = 7³.
The pattern here is that the base of the cube is increased by 3 (4 + 3 = 7), and then cubed.
* 216 is coded as 729.
We know 216 = 6³.
We know 729 = 9³.
Following the same pattern, the base of the cube is increased by 3 (6 + 3 = 9), and then cubed. This confirms the pattern.

Now, apply this pattern to 512:
* 512 = 8³.
* Following the pattern, it should be coded as (8 + 3)³ = 11³.
* 11³ = 11 × 11 × 11 = 121 × 11 = 1331.

Therefore, 512 is written as 1331 in that code. This question tests pattern recognition in number series, a standard reasoning aptitude.