$72519 \times 9999 = x$

### Concept & Formula This involves multiplying a 5-digit number by 9999. We continue applying the algebraic identity for distributive subtraction to minimize calculation time. $$x \times (y - z) = x \times y - x \times z$$ ### Step-by-Step Solution * Rewrite 9999 to its closest base-10 equivalent: $$9999 = 10000 - 1$$ * Apply to the problem: $$72519 \times (10000 - 1)$$ * Distribute 72519: $$725190000 - 72519$$ * Perform the final subtraction: $$725190000 - 72519 = 725117481$$ ### Exam Strategy & Shortcut Since 72519 has 5 digits and 9999 has 4 digits, we append four zeros and subtract the original number. To subtract quickly, look at the last four digits of 725190000, which is 0000. Subtracting 2519 from 10000 yields 7481. The options end in 7481, 6481, etc. Only options (a) and (b) end in 17481. Check the leading digits: $72519 - 7 = 72512$, but with the borrow it becomes $72511$. Thus, the answer starts with 72511. ### Common Pitfall Forgetting to account for the "borrow" across multiple zeros when subtracting, causing an error in the hundreds or thousands place. ### Final Answer **Therefore, the correct answer is 725117481.**