In the following number classification question, four numbers are given (31, 37, 43 and 49). Three of these are prime numbers, while one is a composite number. Select the odd number from the given alternatives.

Introduction / Context:
This is a basic number theory question from the odd man out and series topic. You are given the numbers 31, 37, 43 and 49. Most of these numbers are prime, meaning they have exactly two distinct positive divisors. One number is composite, meaning it has more than two factors. Your task is to identify the composite number as the odd one out.

Given Data / Assumptions:

• Numbers: 31, 37, 43 and 49.
• Prime number: has exactly two positive divisors, 1 and itself.
• Composite number: has more than two positive divisors.
• Exactly one number in the list is composite.
• We only use basic divisibility and factor checks.

Concept / Approach:
The key concept here is the definition of prime and composite numbers. For numbers in the thirties and forties, a quick method is to test divisibility by small primes such as 2, 3, 5 and 7. If a number is not divisible by any of these small primes, and its square root is within that range, the number is prime. If it is divisible by one of these primes, it is composite. By applying this simple test to each option, we can find the number that is not prime.

Step-by-Step Solution:
Step 1: Check 31.31 is not divisible by 2, 3 or 5. 7^2 is 49, which is greater than 31. So 31 has no divisors other than 1 and 31, therefore it is prime.Step 2: Check 37.37 is not divisible by 2, 3 or 5. 7^2 is 49 which is greater than 37, so there are no smaller prime divisors. Therefore 37 is prime.Step 3: Check 43.43 is not divisible by 2, 3 or 5. Next prime 7 gives 7 * 6 = 42, 7 * 7 = 49, so 7 is not a divisor of 43. Hence 43 is also prime.Step 4: Check 49.49 is equal to 7 * 7. It has divisors 1, 7 and 49, so it is clearly composite.Step 5: Identify the odd number.Three numbers (31, 37 and 43) are prime, while 49 is composite. Therefore, 49 is the odd one out.

Verification / Alternative check:
A quick alternative check is to remember squares of small primes. You may know that 7^2 = 49, so 49 must be composite. None of the other numbers is a known square or simple product of small primes, and a rapid divisibility test confirms they are prime. This direct recognition of 49 as a square saves time and strongly supports the answer.

Why Other Options Are Wrong:
31: It is a prime number and fits the majority pattern with 37 and 43.
37: This is also a prime number and therefore not the odd one.
43: Again a prime number, aligning with 31 and 37.

Common Pitfalls:
Some learners may rush and assume that all odd numbers are prime, which is incorrect. Composite odd numbers such as 9, 15 or 49 appear frequently in aptitude tests to trap this misconception. Always apply a quick divisibility check, especially by 3, 5 and 7, before deciding whether a number is prime. Familiarity with the squares of small primes also helps you quickly spot composite numbers like 49.

Final Answer:
The odd number is 49, because 31, 37 and 43 are prime numbers, while 49 is a composite number equal to 7 squared.