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In a code '⊞' means 'is not less than'. Three statements are given, the first and third in ordinary symbols and the second in this code: G > H, 'H ⊞ K', and K = M. What is the relation between G and M?

Competition practiceInequalities
  • AG ≥ M but not necessarily G > M
  • BCannot be determined
  • CG > M
  • DM > G

Step-by-Step Solution

'Is not less than' is ≥, so 'H ⊞ K' decodes to H ≥ K and the three statements read G > H ≥ K = M. Work along it: G > H and H ≥ K give G > K, because a strict link followed by a non-strict one stays strict; then K = M carries that straight over to G > M. 'G ≥ M but not necessarily G > M' is the trap for a solver who lets the non-strict middle link weaken the strict opening link — but strictness is lost only when no strict link is present at all, and here G > H supplies one. 'Cannot be determined' comes from decoding '⊞' as 'is not greater than' and so reversing the middle link. 'M > G' reverses the chain entirely.
Answer: C) G > M

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