Statements: P ≥ R

Question

Statements: P ≥ R < U ≤ M < V; T ≤ U; L < M Conclusion I: V > T Conclusion II: T ≤ P

Accepted Answer

1. From the statements we have $P \ge R < U \le M < V$ and $T \le U$. From $R < U \le M < V$ we note the chain linking $U, M, V$. 2. Combine $T \le U$ with $U \le M < V$ to get $T \le U \le M < V$, which implies $T < V$. Hence $V > T$; conclusion I follows. 3. Conclusion II states $T \le P$. This is not guaranteed by the given relations because $P$ is only constrained by $P \ge R$ while $R < U$; $P$ could be less than $U$ and thus less than $T$. For a concrete counterexample consistent with the statements, take $R=2$, $U=4$, $M=5$, $V=6$, $P=2$ (so $P\ge R$) and $T=4$ (so $T\le U$). Then $T=4> P=2$, so $T \le P$ is false. Thus conclusion II does not necessarily follow. 4. Exactly one of the conclusions follows (I follows, II does not), so the correct choice is: Either conclusion I or conclusion II follow. FINAL_ANSWER: e

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