In a certain code if 64 is written as 343 and 216 is written as 729, then how is 512 written in that code ?
- A1000
- B1331Correct
- C1728
- D2197
Explanation
The numbers in this code follow a pattern involving consecutive perfect cubes.
First, identify the cube root of the given numbers. 64 is the cube of 4. 216 is the cube of 6. 512 is the cube of 8.
Next, look at how they are coded. 64 which is 4 cubed is written as 343 which is 7 cubed. Here, the base increases by 3 from 4 to 7. 216 which is 6 cubed is written as 729 which is 9 cubed. Here, the base increases by 3 from 6 to 9.
Following the same logic for 512: 512 is 8 cubed. Increasing the base 8 by 3 gives us 11. 11 cubed is 11 times 11 times 11, which equals 1331.
Therefore, 512 is written as 1331. The correct option is B.
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