Ages (midpoint relation; information sufficiency): Q is as much younger than R as he is older than T. If R + T = 50 years, what is the difference between R and Q's ages?

Introduction / Context:
Information sufficiency is crucial in age problems. The statement “Q is as much younger than R as he is older than T” implies Q is exactly midway between R and T on the number line of ages. The sum R + T is provided, but no further separation is given.

Given Data / Assumptions:

• R − Q = Q − T ⇒ 2Q = R + T ⇒ Q = (R + T)/2.
• R + T = 50.

Concept / Approach:
Compute Q from the midpoint relation: Q = 25. However, without either R − T or an additional ratio, we cannot pin down R and T individually, hence we cannot determine R − Q uniquely.

Step-by-Step Reasoning:

Verification / Alternative check:
Multiple (R, T) pairs satisfy the constraints and yield different R − Q values, confirming insufficiency.

Why Other Options Are Wrong:
Any specific numeric difference (1, 2, 2.5, 5) asserts extra information not provided by the stem.

Common Pitfalls:
Assuming symmetry further forces R − T = 0, which the problem never states.

Final Answer:
Data inadequate