In the following question, four positive integers are given. Three of them are prime numbers and one is composite. Select the composite number (odd one out).

Introduction / Context:
This odd one out question again focuses on prime and composite numbers, a very important concept in quantitative aptitude. Recognising primes quickly is useful not only in simple classification questions but also in topics like factorisation, modular arithmetic, and number series. The task here is to spot the one composite number among four prime numbers.

Given Data / Assumptions:
- The options are 80, 17, 13, 31, and 19.
- A prime number is greater than 1 and has exactly two positive divisors, 1 and itself.
- A composite number has more than two positive divisors.
- Exactly one number in the given list is composite, and that number is the odd one out.

Concept / Approach:
The most efficient strategy is to check each number for divisibility by small primes such as 2, 3, 5, and 7. If a number is divisible by any of these and is larger than the divisor, it is composite. Small primes like 13, 17, 19, and 31 are well known and often memorised, so identifying them is usually quick. The remaining number that clearly has many factors is the one we should select as the odd one out.

Step-by-Step Solution:
Step 1: Examine 17. It is not divisible by 2, 3, 5, or 7. Therefore, 17 is a prime number.Step 2: Examine 13. It is not divisible by 2, 3, or 5, so it is also a prime number.Step 3: Examine 31. It is not divisible by 2, 3, or 5. It is also not divisible by 7, so 31 is a prime number.Step 4: Examine 19. It is not divisible by 2, 3, or 5, which makes it another prime number.Step 5: Examine 80. It is clearly divisible by 2, since 80 = 2 * 40. It is also divisible by 4, 5, 8, 10, and other numbers. Therefore 80 has many factors and is a composite number.Step 6: Since 17, 13, 31, and 19 are primes while 80 is composite, 80 is the only number that does not belong to the prime group and is the odd one out.

Verification / Alternative Check:
We can verify by listing factors. The factors of 80 include 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80. This confirms that 80 is composite. For 17, the only factors are 1 and 17. For 13, the only factors are 1 and 13. For 31, the only factors are 1 and 31. For 19, the only factors are 1 and 19. Since only 80 has more than two factors, it is correctly identified as the odd one out.

Why Other Options Are Wrong:
17 is not the odd one out because it is a prime and shares this property with 13, 19, and 31. 13 is also prime and fits into the same category. 31 is prime, so it belongs with the other primes. 19 is again prime and therefore not unique in this list. All four of these behave similarly as prime numbers, so none can be chosen as the odd one out.

Common Pitfalls:
Under exam pressure, some candidates might mistakenly classify 19 or 31 as composite because they do not quickly recall their prime status. Others may focus on the size of the numbers instead of checking divisibility. A good practice is to quickly test divisibility by small primes whenever you see an odd one out question based on numbers. This approach ensures that you correctly identify composite numbers like 80 versus prime numbers in the options.

Final Answer:
80