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UPSC Prelims 2025 CSAT, question 66

Topic: Series and patterns

Q66

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) 1331Correct answer
  3. (c) 1728
  4. (d) 2197

Solution.

Answer: (b) 1331

  1. Observe the cube pattern: 64=4364 = 4^3 is coded as 343=73=(4+3)3343 = 7^3 = (4 + 3)^3, and 216=63216 = 6^3 is coded as 729=93=(6+3)3729 = 9^3 = (6 + 3)^3.
  2. Since 512=83512 = 8^3, its code is (8+3)3=113=1331(8 + 3)^3 = 11^3 = 1331.