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Among 6 people, P, Q, R, S, T, and U, each of a different weight, who is the heaviest? I: P is heavier than Q but lighter than R. II: T is heavier than U and S, while R is the lightest of all.
Data in statement I alone is sufficient
Data in statement II alone is sufficient
Data in both statements together are not sufficient
Data in both statements together are sufficient
Data in both statements together are not sufficient
Always check for the presence of all subjects. If the total number of subjects is 6 but the statements collectively don't define the relative position of everyone, the answer is insufficient.
Always check for the presence of all subjects. If the total number of subjects is 6 but the statements collectively don't define the relative position of everyone, the answer is insufficient.
Analyze Statement I
Statement I says P is heavier than Q but lighter than R (R > P > Q). This only involves 3 people and provides no information about T, S, or U.
Analyze Statement II
Statement II says T is heavier than U and S (T > U, T > S) and R is the lightest of all. This relates 4 people but excludes P and Q.
Evaluate Combined Statements
Combining I and II, we know R > P > Q and T > U/S, and R is the lightest. This is a contradiction because Statement I implies R is heavier than P and Q, while Statement II says R is the lightest of all. Even ignoring the contradiction, we lack a definitive link to determine if T is heavier than R.
A: Statement I only provides a partial order of 3 people; B: Statement II only provides a partial order of 4 people; D: Combining them fails to produce a definitive ranking and reveals a contradiction.
C is correct because both statements combined are logically inconsistent and fail to provide enough information to identify the single heaviest individual among all 6 people.
In data sufficiency questions, if statements directly contradict each other or leave variables isolated, they are invariably insufficient.
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