Question: Which train did Harish catch to go to his office? Additional information: Statement A: Harish missed his usual train at 4:15 p.m. Trains arrive every 15 minutes. Statement B: Harish did not catch the 4:45 p.m. train or any train that came after that time. Based on these statements, which option correctly describes the sufficiency of the information?

Introduction / Context:
This is a time table based data sufficiency problem. Harish catches a train to go to his office. The two statements give partial information about which trains he did not catch and how frequently trains arrive. We must decide whether statement A, statement B, or both together are enough to identify exactly which train he boarded.

Given Data / Assumptions:

• Harish usually catches a train at 4:15 p.m.
• Trains arrive every 15 minutes.
• Therefore, trains around that time are at 4:15 p.m., 4:30 p.m., 4:45 p.m., 5:00 p.m., and so on.
• Statement A: Harish missed his usual 4:15 p.m. train.
• Statement B: Harish did not catch the 4:45 p.m. train or any train after 4:45 p.m.

Concept / Approach:
Data sufficiency requires us to decide whether we can narrow the answer down to a single option. If more than one train remains possible after applying a statement, that statement alone is not sufficient. If both statements together narrow the possibilities to one train time, then their combination is sufficient. We are not asked to explain why he caught that train, only to know which one it must be.

Step-by-Step Solution:
Step 1: Using statement A alone. Harish missed his usual 4:15 p.m. train, and trains come every 15 minutes.Step 2: So potential trains he could catch after 4:15 p.m. include the 4:30 p.m. train, the 4:45 p.m. train, the 5:00 p.m. train, and so on.Step 3: Since we have no information on when he actually boarded, multiple possibilities remain. Therefore, statement A alone is not sufficient.Step 4: Using statement B alone. Harish did not catch the 4:45 p.m. train or any train after that time.Step 5: This means he must have caught either the 4:15 p.m. or the 4:30 p.m. train, because later trains are excluded.Step 6: However, we do not know whether he missed the 4:15 p.m. train or not. Therefore, both 4:15 p.m. and 4:30 p.m. are possible boarding times with statement B alone, so it is also not sufficient.Step 7: Now combine statements A and B. Statement A tells us he missed the 4:15 p.m. train. Statement B tells us he did not catch the 4:45 p.m. train or any later train.Step 8: The only remaining train time between 4:15 p.m. and 4:45 p.m. is 4:30 p.m.Step 9: Thus, with both statements together, Harish must have caught the 4:30 p.m. train. There is no other possibility.

Verification / Alternative check:
List all trains: 4:15, 4:30, 4:45, 5:00, and so on.Eliminate 4:15 using statement A. Eliminate 4:45 and later trains using statement B.The only train left that is consistent with both statements is the 4:30 p.m. train, confirming our reasoning.

Why Other Options Are Wrong:
Option a is wrong because statement B alone leaves two possible trains, 4:15 p.m. and 4:30 p.m.Option b is wrong because statement A alone leaves multiple trains after 4:15 p.m.Option d is wrong because together the statements fully determine the train time.Option e is wrong because neither statement alone is sufficient; we need both.

Common Pitfalls:
Not listing all possible train times at 15 minute intervals.Assuming that if a usual train is missed, the next train is always taken, which is not stated.Overlooking that statement B excludes not only 4:45 p.m. but also all trains after that time.

Final Answer:
Therefore, Both statements together are sufficient, but neither statement alone is sufficient to determine which train Harish caught.