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Among 6 people, P, Q, R, S, T and U, each of a different age, who is the youngest? I: Q is older than R but younger than P. S is older than U. II: P is the oldest. U is younger than R.
Data in statement I alone is sufficient
Data in statement II alone is sufficient
Data in both I and II together are sufficient
Data in both I and II together are not sufficient
Data in both I and II together are sufficient
Always combine information from both statements to build a chain of inequality and eliminate everyone except the candidate for the youngest.
Always combine information from both statements to build a chain of inequality and eliminate everyone except the candidate for the youngest.
Analyze Statement I
From statement I, we get the relationships: P > Q > R and S > U. This gives us two separate chains: (P > Q > R) and (S > U). We do not know the relative position of T or the relationship between the two chains, so we cannot determine the youngest.
Analyze Statement II
From statement II, we know P is the oldest and U < R. This gives us P > (others) and R > U. This alone is insufficient as it does not define the positions of Q, S, or T.
Combine Statements I and II
Combining both: P > Q > R and R > U and S > U. Since P is the oldest, the sequence becomes P > Q > R > U and P > S > U. We still have T left. Since the position of T is completely undefined, we cannot determine if T is the youngest or if U is the youngest. Thus, even with both, it is insufficient.
A: Statement I alone is insufficient as it provides fragmented sequences. B: Statement II alone is insufficient as it only defines P and U's relative standing. C: Combining them is insufficient because the position of T is never mentioned, meaning the youngest could be T or U.
D is correct because even after combining all available data, the age of T is unknown relative to the others, preventing the identification of the youngest person.
In data sufficiency questions, if a person or variable mentioned in the question is not mentioned in either statement, the data is usually insufficient.
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