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 ✓ UPSC's answer
- (c) 1728
- (d) 2197
Why the answer is (b)
• 64 = 4³ is written as 343 = 7³, and 216 = 6³ is written as 729 = 9³.
• In both cases the cube root is increased by 3 and the result is cubed.
• 512 = 8³, so its code is (8 + 3)³ = 11³ = 1331, option (b).
Why the other options are wrong
- (a) 1000
- 1000 = 10³ would mean adding 2 to the cube root (8 + 2), but the pattern adds 3.
- (c) 1728
- 1728 = 12³ would mean adding 4 to the cube root (8 + 4), but the pattern adds 3.
- (d) 2197
- 2197 = 13³ would mean adding 5 to the cube root (8 + 5), but the pattern adds 3.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.