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Among 5 friends P, Q, R, S and T, each having a different weight, who is the lightest? I: P is heavier than T but lighter than Q. S is heavier than Q. II: R is the heaviest. T is lighter than P.
Data in statement I alone is sufficient
Data in statement II alone is sufficient
Data in both I and II together are necessary
Data in either I or II is sufficient
Data in both I and II together are necessary
Map the weight inequalities for each statement separately, then merge them; if the position of the lightest person remains ambiguous or constrained, combine both sets of data.
Map the weight inequalities for each statement separately, then merge them; if the position of the lightest person remains ambiguous or constrained, combine both sets of data.
Analyze Statement I
From P is heavier than T but lighter than Q, we get the sequence: Q > P > T. Adding S is heavier than Q, we get: S > Q > P > T. Here, T is the lightest. However, we do not know the position of R.
Analyze Statement II
R is the heaviest. T is lighter than P (P > T). This gives us information about R, P, and T, but leaves the relative positions of Q and S unknown relative to P and T.
Combine Statements I and II
From I, we know S > Q > P > T. From II, we know R is the heaviest. Combining these, the complete order is R > S > Q > P > T. Since T is at the end of the chain, T is definitively the lightest.
A: Statement I alone is insufficient because the position of R is unknown. B: Statement II alone is insufficient because the relationships between Q, S, P, and T are not fully defined. D: Either statement alone is insufficient, making this option logically invalid.
C is correct because both statements combined are necessary to place R as the heaviest and establish the full weight hierarchy showing T is the lightest.
In ranking-based data sufficiency, always check if the variable missing in one statement is provided in the other before concluding insufficiency.
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