In this number series classification question, find the odd number out from the series: 3, 11, 80, 291, 803.

Introduction / Context:
This problem presents a set of numbers 3, 11, 80, 291, 803 and asks you to find the odd one out. Instead of following a stepwise series pattern, we look for a simple divisibility property that one number has and the others do not. Such questions strengthen your ability to quickly scan for distinctive numeric features.

Given Data / Assumptions:

• Numbers: 3, 11, 80, 291, 803
• Exactly one number differs from the others based on an easy-to-check property.
• We consider divisibility by small primes like 2, 3 and 5.

Concept / Approach:
Divisibility tests provide a fast way to classify numbers. In many odd man out questions, the unique number is the only one divisible by a particular prime. Here, we focus on divisibility by 5, which can be identified simply by checking the last digit of each number.

Step-by-Step Solution:
Step 1: Examine the last digit of each number.3 ends with 3.11 ends with 1.80 ends with 0.291 ends with 1.803 ends with 3.Step 2: Apply the rule for divisibility by 5.A number is divisible by 5 if and only if it ends with 0 or 5.Step 3: Identify which numbers are divisible by 5.Only 80 ends with 0 and is divisible by 5. All others end with 1 or 3 and are not divisible by 5.

Verification / Alternative check:
We can quickly confirm by division. 80 / 5 = 16, an exact integer, while 3 / 5, 11 / 5, 291 / 5 and 803 / 5 all produce non-integer quotients. No other simple property such as parity, primality or divisibility by 3 isolates exactly one term as clearly as this test for divisibility by 5.

Why Other Options Are Wrong:
11: Not divisible by 5 and shares this property with 3, 291 and 803.
803: Also not divisible by 5, and cannot be uniquely separated from the others based on this property.
291: Again not divisible by 5 and therefore part of the common group.

Common Pitfalls:
Candidates sometimes search for complex patterns linking all numbers together, for example trying to see polynomial relationships or cumulative sums. However, many odd one out questions rely on very basic arithmetic properties. Ignoring simple divisibility checks can lead to unnecessary confusion and wasted time.

Final Answer:
The odd number out in the given list is 80.