Q. In a certain code if 64 is written as 343 and 216 is written as 729, then how is 512 written in that code?
(a) 1000
(b) 1331
(c) 1728
(d) 2197
Correct Answer : (b) 1331
UPSC Prelims 2025 CSAT
Explanation :
1. Observe that
64 = 4³ and its code 343 = 7³
216 = 6³ and its code 729 = 9³
2. In each case the cube‐root is increased by 3:
4 → 7 (4 + 3 = 7)
6 → 9 (6 + 3 = 9)
3. Apply the same rule to 512:
512 = 8³
Increase 8 by 3 → 11
Cube it → 11³ = 1331
Hence, 512 is written as 1331.
