Directions: Find the odd man out: 385, 462, 572, 396, 427, 671, 264

### Concept & Digit Sum Pattern In certain number series, especially involving $3$-digit numbers, there is a relationship between the digits of each individual number. Here, the middle digit is the sum of the outer two digits (which is also the divisibility rule for $11$). ### Step-by-Step Solution 1. Examine the internal digits of each number: - For $385$: $3 + 5 = 8$ (Middle digit is $8$) - For $462$: $4 + 2 = 6$ (Middle digit is $6$) - For $572$: $5 + 2 = 7$ (Middle digit is $7$) - For $396$: $3 + 6 = 9$ (Middle digit is $9$) - For $671$: $6 + 1 = 7$ (Middle digit is $7$) - For $264$: $2 + 4 = 6$ (Middle digit is $6$) 2. Now check $427$: $4 + 7 = 11$, but the middle digit is $2$. 3. Since $427$ does not follow the "sum of outer digits equals the middle digit" rule, it is the odd one out. ### Exam Strategy & Shortcut When you see $3$-digit numbers that look random and don't have obvious differences, check for multiples of $11$. The fast rule for multiplying a $2$-digit number by $11$ creates exactly this pattern (e.g., $35 \times 11 = 385$). ### Common Pitfall Attempting to find an arithmetic progression (adding or subtracting a constant) across the entire sequence. These types of questions almost always test digit properties or specific divisibility rules. ### Final Answer Therefore, the correct answer is **427**.