Understanding the Data Sufficiency Question

The question asks for the maximum duration Mr. Z might have to wait for a train. This is a Data Sufficiency problem, meaning we need to determine which statement(s), if any, provide enough information to calculate this maximum waiting time.

We are given that trains in Malaysia are very punctual. This implies the trains run on a fixed schedule.

Analyzing the Statements Provided

Let's evaluate each statement and then both statements combined to see if we can find the maximum waiting time for Mr. Z.

Statement 1: Mr. Z had reached the railways station at 10 am

• This statement tells us Mr. Z's arrival time.
• However, it does not provide any information about the train schedule (when the trains depart).
• Without knowing the train schedule, we cannot determine how long Mr. Z will have to wait. He might arrive just before a train, or just after one, leading to different waiting times.
• Therefore, Statement 1 alone is insufficient to answer the question about the maximum waiting time.

Statement 2: There is a train at 11 am and the next train is at 12 pm

• This statement gives us part of the train schedule. It tells us about two specific train departure times.
• However, it does not tell us when Mr. Z arrived at the station.
• If Mr. Z arrived at 10:55 am, his wait for the 11 am train would be only 5 minutes. If he arrived at 11:05 am, he would likely wait for the 12 pm train, meaning a 55-minute wait. The maximum waiting time would depend on his arrival time relative to the schedule.
• Therefore, Statement 2 alone is insufficient to answer the question about the maximum waiting time.

Combining Statements 1 and 2

• From Statement 1, we know Mr. Z arrived at the station at 10 am.
• From Statement 2, we know there is a train at 11 am and the next one is at 12 pm. These are the trains departing after 10 am.
• Since Mr. Z arrived at 10 am, the next available train he can take is the one departing at 11 am.
• The waiting time for Mr. Z would be the difference between the train departure time and his arrival time.
• Waiting time = Train departure time - Arrival time
• Waiting time = 11:00 am - 10:00 am = 1 hour.
• Since the question asks for the maximum time he should wait and the trains are punctual, arriving at 10 am means the earliest he can leave is on the 11 am train. His waiting time is fixed at 1 hour for the next available train. The question could be interpreted as waiting for *a* train after arrival. The most logical waiting time for someone arriving at 10 am, with the next trains at 11 am and 12 pm, is the time until the 11 am train departs.
• Therefore, combining both statements allows us to determine that Mr. Z should wait for the 11 am train, and his waiting time is 1 hour.

Conclusion on Sufficiency

Statement 1 alone is not sufficient. Statement 2 alone is not sufficient. However, both statements combined provide enough information to determine the maximum waiting time for Mr. Z for the next available train, which is 1 hour.

Based on this analysis, both statement 1 and statement 2 are necessary together to answer the question.

Revision Table: Train Waiting Time Problem

Additional Information: Data Sufficiency Strategies

Data Sufficiency questions require a specific approach. Here are some tips:

• Analyze the Question: Understand exactly what needs to be determined.
• Evaluate Statement 1 Alone: Assume only Statement 1 is true. Can you answer the question? If yes, Statement 1 is sufficient.
• Evaluate Statement 2 Alone: Assume only Statement 2 is true (ignore Statement 1 for now). Can you answer the question? If yes, Statement 2 is sufficient.
• Evaluate Statements 1 and 2 Together: If neither statement alone was sufficient, combine the information from both. Can you answer the question now?
• Determine Sufficiency: Based on the above steps, choose the correct option (Statement 1 alone, Statement 2 alone, Both needed, Either one is sufficient, Neither is sufficient).
• Avoid Solving: You don't always need to find the exact numerical answer, just determine if it *can* be found. However, for verification, sometimes calculating the answer helps confirm sufficiency.

In this problem, the maximum waiting time for Mr. Z, given his arrival at 10 am and the next train at 11 am, is indeed 1 hour. This calculation was only possible by combining both pieces of information.