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Among 5 friends, P, Q, R, S and T, each having a different weight, who is the lightest? Statement I: P is heavier than T but lighter than Q. R is heavier than Q. Statement II: S is the heaviest among all. T is lighter than Q and P.
Data in statement I alone is sufficient
Data in statement II alone is sufficient
Data in both statements together are necessary
Data in either statement alone is sufficient
Data in both statements together are necessary
Write out the inequality chain for each statement independently to see if all 5 variables connect into a single ordered sequence.
Write out the inequality chain for each statement independently to see if all 5 variables connect into a single ordered sequence.
Analyze Statement I
Statement I gives: P > T, Q > P, so Q > P > T. Also R > Q, so R > Q > P > T. However, the position of S is completely unknown. Thus, Statement I alone is insufficient to find the lightest.
Analyze Statement II
Statement II gives: S is the heaviest. Also Q > T and P > T (so Q, P > T). But the relative order between Q, P, and R is not fully known. Thus, Statement II alone is insufficient.
Combine Both Statements
From Statement I and II combined: S is heaviest. R > Q > P > T. Since T is the smallest in the entire chain (S > R > Q > P > T), T is uniquely identified as the lightest.
A: Statement I alone cannot determine the position of S, so it is incorrect. B: Statement II alone leaves the relative order of R, Q, and P ambiguous and fails to identify the lightest uniquely, so it is incorrect. D: Since neither statement alone is sufficient, D is incorrect.
C is correct because combining both statements gives the complete descending weight order of S > R > Q > P > T, clearly showing that T is the lightest.
In data sufficiency ranking problems, always evaluate each statement independently first before combining them to avoid biased conclusions.
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