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Take the chain below exactly as written — no other information is available.
Statement: G < H ≥ K < L
Conclusions: I. G < K
II. H > L
Which conclusion follows?

Competition practiceInequalities
  • AOnly I follows
  • BBoth I and II follow
  • CNeither I nor II follows
  • DOnly II follows

Step-by-Step Solution

G < H and H ≥ K both point up towards H, so H is above both G and K but the two of them are never compared: G = 1, H = 9, K = 2 makes I true, while G = 5, H = 9, K = 2 makes it false. So I does not follow. Likewise H ≥ K and K < L both leave L free: H = 9, K = 2, L = 3 makes II true, but H = 9, K = 2, L = 40 makes it false. Neither follows. 'Only I follows' is precisely what a solver gets by misreading H ≥ K as K ≥ H, since G < H ≤ K really would give G < K. 'Both' comes from treating the whole line as one descending run and ignoring both reversals.
Answer: C) Neither I nor II follows

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