Directions: Find the odd man out: 1, 4, 9, 16, 23, 25, 36

### Concept & Perfect Squares The sequence is formed by the squares of consecutive natural numbers. Identifying perfect squares is a fundamental skill for number series. $$n^2$$ ### Step-by-Step Solution 1. Analyze the terms: $1, 4, 9, 16, 23, 25, 36$. 2. Express them as powers: - $1 = 1^2$ - $4 = 2^2$ - $9 = 3^2$ - $16 = 4^2$ - $25 = 5^2$ - $36 = 6^2$ 3. The number $23$ falls between $16$ and $25$ but is not the square of any integer. 4. Thus, $23$ disrupts the sequence of perfect squares. ### Exam Strategy & Shortcut Memorize perfect squares up to at least $30^2$. When you see $1, 4, 9, 16$, your brain should immediately recognize the perfect square pattern and flag $23$ as the anomaly. ### Common Pitfall Assuming the sequence might represent a mixed arithmetic progression and wasting time calculating differences ($+3, +5, +7, +7, +2, +11$) which leads to a dead end. ### Final Answer Therefore, the correct answer is **23**.