Direction: Study the following information and answer the question that follows: P, Q, R,...
Qualcomm technical mcq question, verified with a worked answer. Free to practise - no sign-up.
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 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 constraint vi), R is younger than only one person, meaning R is the second-oldest. From constraints i) and iv), we establish the age ordering: S > U > R, with P < S and Q < R. Working through all constraints, S must be the oldest person. Constraint viii) states the oldest is not the heaviest, so S is not the heaviest despite being oldest—a unique distinguishing property that makes S the answer.
Step-by-step Derivation:
Step 1: Extract age relationships:
- From (i): P < S (age)
- From (ii): Q < R (age)
- From (iii): U < Q and U < R (age)
- From (iv): S < U (age)
- From (vi): R is younger than exactly one person → R is 2nd oldest
Step 2: Combine (iv) and (vi):
- S < U and R is 2nd oldest → S must be oldest (1st), U must be 3rd or lower
- Since U < Q, U < R, and R is 2nd oldest → U is 3rd oldest
- Ordering so far: S (oldest) > R (2nd) > U (3rd)
Step 3: Place remaining members:
- From (i): P < S ✓
- From (ii): Q < R ✓
- From (iii): U < Q, so Q > U ✓
- Age order: S > R > U > Q and P somewhere (P < S)
- Since U < Q and R is 2nd, and U is 3rd: Q must be 4th or 5th
- Likely: S > R > U > Q > P > T or similar
Step 4: Weight relationships:
- From (v): P > R > Q (weight)
- From (ii): Q > T (weight)
- From (iii): U > T and U > Q (weight)
- From (vii): U < R (weight)
- Weight order: P > R > U > Q > T (satisfies all constraints)
Step 5: Apply constraint (viii):
- S is oldest (age ranking)
- Weight order is P > R > U > Q > T
- S's weight is not determined but must fit the order
- S is not the heaviest (P is)
- Therefore, S is the oldest but not the heaviest—a unique distinguishing characteristic.
Answer: S (option B)