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?
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A2.5 years
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B2 years
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C1 years
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DData inadequate
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E5 years
Answer
Correct Answer: Data inadequate
Explanation
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:
From 2Q = R + T and R + T = 50 ⇒ Q = 25. But R − Q = (R − 25) can vary while keeping R + T fixed at 50 (e.g., R = 30 gives R − Q = 5; R = 28 gives 3).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