Select the synonym of the word "metropolitan" in the sense of being related to a city or sophisticated urban life.

Introduction / Context:
This vocabulary question asks you to find the synonym of "metropolitan". The word "metropolitan" usually refers to something connected with a large city, especially in contrast to rural areas. It can also carry a nuance of being polished or sophisticated in manners typical of large urban centres. You have to choose the option that best captures this sense.

Given Data / Assumptions:

• The key word is "metropolitan".
• Options given are "idyllic", "arcadian", "bucolic", and "urbane".
• We assume the exam is using the common meaning of "metropolitan" linked to cities and city style.

Concept / Approach:
The approach to synonym questions is:

• Recall the core meanings and typical usage of the target word.
• Check which option has a similar core meaning and not merely a weak association.
• Be careful with words that describe the opposite setting, such as countryside versus city.

"Metropolitan" is often contrasted with "rural", "rustic", or "pastoral".

Step-by-Step Solution:
Step 1: Understand "metropolitan": it relates to a large city, a metropolis, and often suggests sophistication, modernity, and urban culture. Step 2: Look at "idyllic". It describes a place that is peaceful and charming in a simple, often rural way. This is generally opposite to busy city life. Step 3: Consider "arcadian". This word refers to an idealized rural or pastoral setting, again strongly connected to countryside simplicity. Step 4: Examine "bucolic". It also means rustic or relating to the pleasant aspects of country life. Step 5: Finally, look at "urbane". It describes a person as polished, refined, and sophisticated, typically in the way someone from a big city might be. Step 6: Among these, "urbane" shares the idea of city based refinement that lies inside the idea of "metropolitan".

Verification / Alternative check:
Think of pairs: "metropolitan" versus "rural" or "bucolic". The three options "idyllic", "arcadian", and "bucolic" all clearly belong to the rural, countryside family of meanings. "Urbane", however, comes from "urban" and strongly suggests city culture and manners. Therefore it aligns best with the sense of "metropolitan" used in competitive exams when contrasted with a village or rural background.

Why Other Options Are Wrong:

• idyllic: Suggests simple, peaceful rural beauty, the opposite of crowded metropolitan life.
• arcadian: Refers to an ideal rustic paradise, again connected to the countryside.
• bucolic: Directly means relating to pleasant country life and shepherds, not cities.

Common Pitfalls:
A common misconception is to treat "metropolitan" only as "large and pleasant" and then choose any positive sounding adjective. But vocabulary questions depend on precise context: metropolitan areas form the opposite of bucolic, pastoral regions. Remember to connect "metro" with "urban" and keep rural related adjectives clearly separate in your mind.

Final Answer:
The correct synonym for "metropolitan" in this context is urbane.