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

Mental Ability & Logical Reasoning ·Previously asked in UPSC Civil Services Examination 2025

View the full solved paper: GS Paper II

Question

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 (Correct answer)
  3. C. 1728
  4. D. 2197

Correct Answer

Option B — 1331

Detailed Solution & Explanation

The correct answer is 1331.

Key Points

  • 64=4³ is coded as 343=7³.
  • 216=6³ is coded as 729=9³.
  • Pattern: cube root + 3, then cubed. ∛64=4 → 4+3=7 → 7³=343. ∛216=6 → 6+3=9 → 9³=729.
  • 512=8³ → 8+3=11 → 11³=1331. Answer: 1331.