Q56. 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?
Detailed Solution
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.
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