Classification — identify the odd number: which one does NOT satisfy the shared property of the other three numbers?

Introduction / Context:
Odd-one-out classification questions test whether you can quickly detect a hidden property shared by most items and then eliminate the exception. A reliable strategy is to scan for simple numeric properties first (such as divisibility by 2, 3, 5, or 9) before attempting more exotic patterns.

Given Data / Assumptions:

• Choices: 531, 243, 413, 612.
• All are three-digit positive integers.
• We assume the task is to find exactly one number that does not share the others’ common property.

Concept / Approach:
Start with classic divisibility checks. Divisibility by 3 is especially fast via the digit-sum test: a number is divisible by 3 if the sum of its digits is a multiple of 3. If three numbers pass and one fails, the non-multiple of 3 is the odd one out.

Step-by-Step Solution:
1) 531 → digit sum = 5 + 3 + 1 = 9, and 9 is divisible by 3 ⇒ 531 is divisible by 3.2) 243 → digit sum = 2 + 4 + 3 = 9 ⇒ divisible by 3.3) 612 → digit sum = 6 + 1 + 2 = 9 ⇒ divisible by 3.4) 413 → digit sum = 4 + 1 + 3 = 8 ⇒ not divisible by 3.5) Therefore, three numbers are multiples of 3; 413 is the only one that is not.

Verification / Alternative check:
You can also divide directly: 531/3 = 177, 243/3 = 81, 612/3 = 204; 413/3 is not an integer. This confirms that 413 is uniquely not a multiple of 3.

Why Other Options Are Wrong:
531, 243, and 612 each share the common property (divisible by 3). Since the problem asks for the non-conforming number, these are not correct choices.

Common Pitfalls:
Overcomplicating with patterns like “first two digits sum to the third.” Quick divisibility tests are designed for speed and accuracy; try them before complex heuristics.

Final Answer:
413