Directions: Find the odd man out: 8, 27, 64, 100, 125, 216, 343

### Concept & Perfect Cubes The pattern relies on recognizing perfect cubes of integers. A perfect cube is formed by multiplying an integer by itself twice. $$n^3$$ ### Step-by-Step Solution 1. Review the sequence: $8, 27, 64, 100, 125, 216, 343$. 2. Express the numbers as powers: - $8 = 2^3$ - $27 = 3^3$ - $64 = 4^3$ - $125 = 5^3$ - $216 = 6^3$ - $343 = 7^3$ 3. Evaluate the number $100$. It is a perfect square ($10^2$), but it is not a perfect cube. 4. Hence, $100$ breaks the pattern of perfect cubes. ### Exam Strategy & Shortcut Memorizing perfect cubes up to $10^3$ is crucial for speed. If you know them, $100$ stands out instantly as a square placed amongst cubes. ### Common Pitfall Mistaking $100$ for a valid entry simply because it is a "special" or "round" number, or confusing perfect squares with perfect cubes under exam pressure. ### Final Answer Therefore, the correct answer is **100**.