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The relations below are given in words rather than symbols. K is at least as large as L. L is not smaller than M. M is larger than N. Which of the following is definitely true?

Competition practiceInequalities
  • AL > N
  • BN > K
  • C
  • DM ≥ K

Step-by-Step Solution

Translate first: "at least as large as" and "not smaller than" are both ≥, so the statements are K ≥ L, L ≥ M and M > N, giving the single chain K ≥ L ≥ M > N. Reading from L rightwards, L ≥ M and M > N, and a strict link anywhere in a descending run makes the whole run strict, so L > N is forced. N > K reverses a chain that only ever descends, so it is false outright. K = M and M ≥ K both fail because K ≥ L ≥ M leaves K above M with room to spare: K = 9, L = 5, M = 5, N = 1 satisfies every statement and makes each of them false, while K = L = M = 5 with N = 1 would make them true — so neither is forced.
Answer: A) L > N

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