Select the odd number from the following alternatives based on whether it is prime or composite.

Introduction / Context:
This number reasoning question checks your understanding of prime and composite numbers. Prime numbers play a central role in number theory and frequently appear in aptitude questions, so being able to quickly separate primes from composites is a useful exam skill.

Given Data / Assumptions:

• The four numbers given are: 43, 22, 13, and 41.
• You must select the number that does not share the same nature as the others.
• Assume standard definitions of prime and composite numbers.

Concept / Approach:
A prime number is a positive integer greater than 1 that has exactly two distinct positive factors: 1 and the number itself. A composite number has more than two factors. The standard method is to test each number for divisibility by smaller primes and identify which numbers are prime and which are composite.

Step-by-Step Solution:
Step 1: Check 43. It is not divisible by 2, 3, 5, or 7, and no smaller prime divides it. So 43 is a prime number. Step 2: Check 13. It is not divisible by 2, 3, or 5, and again it has no factors other than 1 and 13, so 13 is prime. Step 3: Check 41. It is not divisible by 2, 3, or 5, and there is no smaller divisor, so 41 is also a prime number. Step 4: Check 22. It is divisible by 2 and 11, so it has factors 1, 2, 11, and 22, meaning it is a composite number. Step 5: Three of the numbers are prime, and one number is composite. Therefore, the composite number is the odd one out.

Verification / Alternative check:
You can quickly verify your conclusion by checking divisibility rules. Any even number greater than 2 is automatically composite. Here, 22 is even, so it must be composite. The other numbers are odd and fail simple divisibility checks for small primes, which supports the conclusion that they are primes. This gives a fast alternative confirmation.

Why Other Options Are Wrong:

• 43: This is a prime and shares the same property as 13 and 41, so it is not the odd number.
• 13: This is clearly a prime, so it matches the majority group.
• 41: This is another prime number, so it also belongs with the majority.

Common Pitfalls:
Sometimes learners quickly look at the size or parity of the numbers and may mistakenly treat all odd numbers as prime. However, not every odd number is prime, and not every even number is composite except 2. Here, paying attention to divisibility rules is essential, and recognizing that 22 is even immediately signals that it is composite.

Final Answer:
22