Product of $82540027$ and $43253$ is

### Concept & Logic This problem asks for the product of two extremely large numbers. In banking and aptitude exams, such questions are intentionally designed to test your observational skills rather than your ability to perform tedious multiplication. ### Step-by-Step Solution * **Given:** Multiply $82540027$ by $43253$. * **Step 1:** Extract the unit digits of both numbers. Number 1 unit digit: $7$ Number 2 unit digit: $3$ * **Step 2:** Multiply the unit digits together. $7 \times 3 = 21$ * **Step 3:** Identify the final unit digit of the product. The product must end in $1$. * **Step 4:** Evaluate the given options based on their last digit. (a) ends in 1 (b) ends in 2 (c) ends in 3 (d) ends in 4 * **Step 5:** Since only one option matches the required unit digit, it must be the correct answer. ### Exam Strategy & Shortcut Do not even write the numbers down. The moment you see options that are identical except for their final digit, simply multiply the last digits of the given numbers ($7 \times 3 = 21$). The answer ends in $1$. Option (a) is the only one. Total time taken: 2 seconds. ### Common Pitfall A major pitfall is initiating the long multiplication out of habit or panic, not realizing the options differ strictly by a single digit at the very end. Always scan the options before starting a heavy calculation. ### Final Answer Therefore, the correct answer is **3570103787831**.