Directions: Find the odd man out: 3, 5, 7, 12, 17, 19

### Concept & Number Properties The core concept here revolves around prime and composite numbers. A prime number has only two divisors: $1$ and itself. ### Step-by-Step Solution 1. Analyze the given sequence: $3, 5, 7, 12, 17, 19$. 2. Check the properties of each number: - $3$ is a prime number. - $5$ is a prime number. - $7$ is a prime number. - $17$ is a prime number. - $19$ is a prime number. 3. Observe the number $12$. It is divisible by $1, 2, 3, 4, 6,$ and $12$, making it a composite number. 4. Therefore, $12$ does not belong to the group of prime numbers. ### Exam Strategy & Shortcut Whenever you see a series of numbers that don't have a consistent arithmetic or geometric difference, quickly check for squares, cubes, and prime/composite properties. Identifying primes is usually the fastest route. ### Common Pitfall Students may try to find complex subtraction/addition patterns (e.g., $+2, +2, +5, +5, +2$) and get stuck when the pattern fails, instead of looking at the fundamental property of the numbers. ### Final Answer Therefore, the correct answer is **12**.