If the largest three-digit number is subtracted from the smallest five-digit number, then the remainder is

### Concept & Logic This problem requires correctly identifying boundary numbers based on digit counts and performing basic subtraction. ### Step-by-Step Solution **Calculation:** 1. Formulate the smallest 5-digit number: A $1$ followed by four zeros ($10000$). 2. Formulate the largest 3-digit number: Three $9$s ($999$). 3. Subtract the 3-digit number from the 5-digit number: $$10000 - 999 = 9001$$ ### Exam Strategy & Shortcut Instead of standard subtraction with borrowing, use the round-number approximation. Treat $999$ as $(1000 - 1)$. Equation becomes: $10000 - (1000 - 1) = 9000 + 1 = 9001$. This eliminates calculation errors completely. ### Common Pitfall Miscounting the zeros in the smallest 5-digit number (using $1000$ instead of $10000$) will lead to $1000 - 999 = 1$, which is a trap option deliberately provided as Option A. ### Final Answer Therefore, the correct answer is **9001**.