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Three separate facts are recorded: V > W, W = X, and X ≥ Y. What is the relation between V and Y?

Competition practiceInequalities
  • AV > Y
  • BV ≥ Y but not necessarily V > Y
  • C
  • DCannot be determined

Step-by-Step Solution

The three statements share the intermediate variables W and X, so they compose into one run: V > W, then W = X passes the relation across unchanged, then X ≥ Y. That is V > X ≥ Y, and a strict link followed by a non-strict one composes to strict, so V > Y. 'V ≥ Y but not necessarily V > Y' is the trap for a solver who thinks the trailing non-strict link X ≥ Y drags the whole result down to ≥; in fact strictness survives as long as at least one link in the run is strict, and V > W is strict. 'Cannot be determined' comes from treating the equality as a dead end instead of a pass-through. 'V = Y' would require every link to be an equality, but V > W rules that out.
Answer: A) V > Y

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