Direction: Study the following information and answer the question that follows: P, Q, R,...
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Direction:** Study the following information and answer the question that follows:
P, Q, R, S, T and U are 6 members within a committee. The six members differ in their ages and weights.
i) P is younger than S.
ii) Q is heavier than T and younger than R.
iii) U is heavier than T and but younger than Q and R.
iv) U is older than S.
v) P is heavier than R, who is heavier than Q.
vi) R is younger than only one person.
vii) U is lighter than R.
viii) The oldest one is not the heaviest.
Show answer & explanation
From constraint (vi), R is younger than only one person, meaning R is the second oldest. From constraint (iv), U is older than S, and from constraint (i), P is younger than S. From constraint (iii), U is younger than Q and R. Since R is second oldest and U < Q, R, the only person older than R must be someone not yet placed at the top. Working through all constraints systematically: the age ordering is S > R > U > Q > P > T, making S the oldest person.
Step-by-step Derivation:
Step 1: From (vi), R is younger than exactly one person → R is second oldest.
Step 2: From (iii), U < Q and U < R. From (iv), U > S. From (i), P < S.
Step 3: From (ii), Q < R. Combined with (iii), we have U < Q < R.
Step 4: From (i) and (iv): P < S and U > S, so U > S > P.
Step 5: Since R is second oldest, the oldest must be someone older than R. Given U > S, U > P, and the remaining person T must fit. From (ii), Q is younger than R, so Q cannot be oldest.
Step 6: Since U is older than S but younger than R (from iii), and R is second oldest, S must be the oldest.
Step 7: Final age order: S (oldest) > R > U > Q > P > T. This satisfies all constraints.
Step 8: Verify (viii): S is oldest but checking weights: P > R > Q and U > T, U < R. So P is heaviest, not S. ✓
Answer: S is the oldest.