$884697 - 773697 - 102479 = x$

### Concept & Strategy This is a multi-step subtraction problem. The fastest approach relies on recognizing specific number patterns to simplify mental math, grouping terms to reduce the number of borrowing steps. ### Step-by-Step Solution * **Given:** The continuous subtraction $884697 - 773697 - 102479$. * **Step 1:** Notice that the first two numbers share the same last three digits ($697$). Subtracting them sequentially is much faster than summing the negative components first. $884697 - 773697$ * **Step 2:** Calculate the difference. Since $697 - 697 = 000$, just subtract the thousands: $884 - 773 = 111$. The result is $111000$. * **Step 3:** Subtract the final number from this intermediate result. $111000 - 102479$ * **Step 4:** Perform the subtraction. You can break it down logically: $111000 - 102000 = 9000$ $9000 - 479 = 8521$ ### Exam Strategy & Shortcut Once you see $884697 - 773697 = 111000$, look at the last number: $102479$. You just need to calculate $111000 - 102479$. Use the **complement method** for the last three digits: $1000 - 479 = 521$. The answer must end in $521$. Looking at the options, only (c) ends in $521$. You can mark it instantly without completing the full calculation. ### Common Pitfall A common error is summing $773697$ and $102479$ first. While mathematically sound, it involves heavier carrying and borrowing, consuming far more time than simply recognizing the $697$ cancellation in the first step. ### Final Answer Therefore, the correct answer is **8521**.