Which digits should come in place of $*$ and $\$$ if the number $62684*\$$ is divisible by both $8$ and $5$?

### Concept & Logic This problem requires applying the divisibility rules for both $5$ and $8$. A number is divisible by $5$ if its last digit is $0$ or $5$. A number is divisible by $8$ if the number formed by its last three digits is divisible by $8$. ### Step-by-Step Solution **Given:** The number is $62684*\$$. It must be divisible by $5$ and $8$. **Calculation:** Step 1: Determine $\$$ using the rule for $5$. The last digit $\$$ must be $0$ or $5$. However, an even divisor like $8$ can only divide even numbers. A number ending in $5$ is odd. Thus, $\$$ must be $0$. The number is now $62684*0$. Step 2: Determine $*$ using the rule for $8$. The last three digits form the number $4*0$. We need $4*0$ to be divisible by $8$. Substitute $*$ with digits from the options: If $*$ is $4$, the number is $440$. $440 / 8 = 55$. This is perfectly divisible. ### Exam Strategy & Shortcut Immediately deduce that the final digit of any number divisible by an even number must be even. Therefore, $\$$ cannot be $5$, it must be $0$. This allows you to instantly eliminate options B and D. Then, plug in the remaining possible values for $*$ into the last three digits ($4*0$) to find the match. ### Common Pitfall Students often try to test for the divisibility of $8$ before securing the unit digit. Fixing the most restrictive condition first (the unit digit) drastically reduces the number of possibilities you have to check. ### Final Answer Therefore, the correct answer is **4 and 0**.