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.
Conditions:
i) P is younger than S.
ii) Q is heavier than T and younger than R.
iii) U is heavier than T and Q 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 condition (vi), R is younger than only one person, meaning R is the second-oldest. From condition (iv), U is older than S, and from condition (i), P is younger than S. From condition (iii), U is younger than Q and R, but from condition (ii), Q is younger than R. Combining these constraints: Q is younger than R (condition ii), and R is younger than only one person (condition vi, meaning only one person is older than R). This places Q as the youngest since Q must be younger than all others based on the age constraints.
Step-by-step Derivation:
Step 1: From condition (vi): R is younger than only one person → only one person is older than R.
Step 2: From condition (iii): U < Q and U < R (in age).
Step 3: From condition (ii): Q < R (in age).
Step 4: From condition (iv): S < U (in age).
Step 5: From condition (i): P < S (in age).
Step 6: Ordering from Step 1: Since R is second-oldest, someone is older than R. From conditions (iii) and (iv), U > S and S > P, so U could be the oldest.
Step 7: Since U > S > P and U > Q, R > Q, and only R is younger than one person (U), the age order is: U > R > S > (P and Q must be ordered). From condition (i), P < S, so P < S. From condition (iii), U < Q is FALSE (U > Q from the constraint that U is older than Q in weight context, but age-wise U > S > P and Q < R < U).
Step 8: Re-examining: Q < R, U < Q is FALSE. So U > Q. Combined with S > P, U > S, and R is second oldest: Age order = U > R > S > P > Q. Therefore Q is youngest.