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Among five boxes P, Q, R, S, and T, which one is the heaviest? (I) P is heavier than Q and R. (II) T is heavier than S but lighter than Q.
Data in (I) alone is sufficient
Data in (II) alone is sufficient
Data in both (I) and (II) together are not sufficient
Data in both (I) and (II) together are sufficient
Data in both (I) and (II) together are sufficient
Always represent weights as an inequality chain; if you cannot pin down the heaviest variable at the extreme end of the chain, the data is insufficient.
Always represent weights as an inequality chain; if you cannot pin down the heaviest variable at the extreme end of the chain, the data is insufficient.
Analyze Statement I
From statement I, we have P > Q and P > R. P is heavier than Q and R, but we do not know the relation between P, S, and T.
Analyze Statement II
From statement II, we have Q > T > S. This tells us about the relative weights of Q, T, and S, but provides no information about P or R.
Combine Statements
Combining both, we get the sequence: P > Q > T > S. Also, we know P > R. We have the sequence P > {Q, R} and Q > T > S. Combining these, P > Q > T > S and P > R. Since P is heavier than Q and Q is heavier than T and S, and P is also heavier than R, P must be the heaviest.
A: Statement I alone only establishes P is heavier than Q and R, leaving the position of S and T unknown relative to P. B: Statement II alone only gives the order Q > T > S, providing no info on P or R. C: Both statements together successfully establish that P is greater than all others.
D is correct because combining both statements establishes the complete chain P > Q > T > S and P > R, clearly identifying P as the heaviest.
In comparison puzzles, look for a common variable between statements; if no variable links them, you cannot form a sequence and the data remains insufficient.
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