The number 89715938* is divisible by 4. The unknown non-zero digit marked as * will be

### Concept & Formula The divisibility rule for $4$ dictates that a number is divisible by $4$ if and only if the number formed by its last two digits is divisible by $4$. ### Step-by-Step Solution * **Given:** The number is $89715938*$. The last two digits form the number $8*$, where $*$ represents a single digit. * **Calculation:** We need to find which option can replace $*$ such that $8*$ is a multiple of $4$. Let us evaluate the given choices: If $* = 2$, the number is $82$. ($82 / 4 = 20.5 \rightarrow$ Not divisible) If $* = 3$, the number is $83$. (Odd number $\rightarrow$ Not divisible) If $* = 4$, the number is $84$. ($84 / 4 = 21 \rightarrow$ **Divisible**) If $* = 6$, the number is $86$. ($86 / 4 = 21.5 \rightarrow$ Not divisible) Only substituting $4$ creates a valid multiple. ### Exam Strategy & Shortcut You can eliminate odd numbers instantly. Since $4$ is even, any multiple of $4$ must also be even, eliminating option (b). Furthermore, if the tens digit is even (like $8$), the unit digit MUST be $0, 4, \text{or} 8$ to be a multiple of $4$. This immediately singles out $4$ as the only mathematically sound option. ### Common Pitfall Some test-takers confuse the rule for $4$ with the rule for $8$ (last three digits) or $3$ (sum of all digits). Trying to sum the entire string of $89715938*$ will waste immense time and lead to a completely incorrect framework. ### Final Answer Therefore, the correct answer is **4**.