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For which one of the following chains does the conclusion P > T definitely follow?

Competition practiceInequalities
  • AP ≥ Q > R = T
  • BP ≥ Q ≥ R ≥ T
  • CP > Q ≤ R = T
  • DP = Q ≥ R ≥ T

Step-by-Step Solution

A strict conclusion needs a run whose links all point the same way and of which at least one is strict. 'P ≥ Q > R = T' meets both tests: the links descend throughout and Q > R is strict, so composing gives P > R = T, hence P > T. 'P ≥ Q ≥ R ≥ T' descends but contains no strict link, so it yields only P ≥ T — P = Q = R = T = 4 satisfies it and refutes P > T. 'P = Q ≥ R ≥ T' fails for the same reason. 'P > Q ≤ R = T' has a strict link but the sense reverses at Q, so P and T are never compared: P = 9, Q = 1, R = T = 2 gives P > T, while P = 3, Q = 1, R = T = 40 satisfies the chain and gives P < T.
Answer: A) P ≥ Q > R = T

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