Data Sufficiency — Train selection by time: Which train did Aman catch to go to office? Statements: I. Aman missed his usual 10:25 a.m. train. II. A train arrives every 5 minutes. Aman did not catch the 10:40 a.m. train or any train after that.

Introduction / Context:We need to identify the exact train Aman boarded. Trains run at regular 5-minute intervals. Data sufficiency requires a unique determination; if multiple trains fit the conditions, the data are insufficient.

Given Data / Assumptions:

• I: Aman missed 10:25 a.m. (his usual train).
• II: Trains every 5 minutes; Aman did not take the 10:40 a.m. or any later train.
• Typical sequence near that time: 10:25, 10:30, 10:35, 10:40, 10:45, …

Concept / Approach:List feasible trains that respect both constraints. If more than one remains, the answer is not uniquely determined and the correct sufficiency choice is “Neither”.

Step-by-Step Solution:From I: Aman did not take 10:25.From II: Aman did not take 10:40 or anything later.Feasible trains between 10:25 (excluded) and 10:40 (excluded): 10:30 and 10:35.Two candidates remain; the data do not single out one train.

Verification / Alternative check:Unless an extra condition (e.g., “he boarded the earliest possible train”) is given, both 10:30 and 10:35 satisfy all provided constraints. Therefore, insufficiency is conclusive.

Why Other Options Are Wrong:

• I alone: Gives only one exclusion (10:25).
• II alone: Excludes 10:40 and later, leaving many possibilities before 10:40.
• Either / Both: Even together, ambiguity remains between 10:30 and 10:35.

Common Pitfalls:

• Assuming Aman always takes the immediate next train—this is not stated.
• Overlooking that two qualifying times exist within the window.

Final Answer:Neither I nor II is sufficient