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Read the line below as one continuous chain of true relations.
Statement: U ≤ V < W ≥ X
Conclusions: I. U < X
II. V ≥ X
Which conclusion follows?

Competition practiceInequalities
  • ANeither I nor II follows
  • BOnly I follows
  • COnly II follows
  • DBoth I and II follow

Step-by-Step Solution

The chain rises from U to W and then falls to X, so W is above everything and U, V, X are never linked to one another. Test I: U = 1, V = 2, W = 9, X = 8 gives U < X, but U = 7, V = 8, W = 9, X = 1 satisfies every statement and gives U > X, so I does not follow. Test II with the same two sets of values: V = 8 and X = 1 makes V ≥ X true, while V = 2 and X = 8 makes it false, so II does not follow either. 'Only II follows' is what a solver gets by misreading W ≥ X as X ≥ W, since V < W ≤ X would at least link V and X — though even then it would give V < X, not V ≥ X. 'Both' comes from reading the line as one rising run and ignoring the reversal at W.
Answer: A) Neither I nor II follows

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