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Among 5 friends P, Q, R, S and T, each having different weights, who is the lightest? Statement I: P is heavier than Q but lighter than T. R is heavier than S. Statement II: Q is heavier than S. T is the heaviest among all.
Data in statement I alone is sufficient
Data in statement II alone is sufficient
Data in both statements together are sufficient
Data in both statements together are not sufficient
Data in both statements together are sufficient
Map the inequalities as a single chain: if Statement I gives a partial segment and Statement II provides the anchor (heaviest) and a connector, combine them to complete the sequence.
Map the inequalities as a single chain: if Statement I gives a partial segment and Statement II provides the anchor (heaviest) and a connector, combine them to complete the sequence.
Analyze Statement I
From Statement I: T > P > Q and R > S. We have two separate segments: (T, P, Q) and (R, S). We cannot determine the position of R or S relative to P, Q, or T, so Statement I alone is insufficient.
Analyze Statement II
Statement II states Q > S and T is the heaviest. We know T > (P, Q, R, S) and Q > S. Without knowing the relationship between P and R or P and S, we cannot determine the lightest, so Statement II alone is insufficient.
Combine Statements I and II
From I: T > P > Q; R > S. From II: Q > S and T is heaviest. Combining these: T > P > Q > S. Since R > S and we know T is the heaviest (T is above R), we look for the relationship between R and the rest. The chain results in T > (P, R) > Q > S. Since S is at the bottom of the Q > S chain and no one else is confirmed lighter than S, S is the lightest.
A: Statement I fails to connect R and S to the P-Q-T group. B: Statement II gives the heaviest but does not define the full order for the lighter end. D: Both together successfully establish S as the lightest through the chained inequalities.
C is correct because combining both statements allows us to form the inequality chain T > P > Q > S and R > S, identifying S as the lightest member.
In ranking-based data sufficiency, always look for the common element (the link) between statements that allows you to join independent chains into one.
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