Question

The number $89715938 * $ is divisible by 4. The unknown non – zero digit marked as $\left( * \right)$ will be
A.2
B.3
C.4
D.6

Answer 1

Hint: We will use the property of divisibility by 4 given as: a number (with 3 or more digits) is divisible by 4 if the number formed by the last two digits of the number is divisible by 4. We will check for every option if the number formed by them are divisible by 4 or not.

Complete step-by-step answer:
We are given a number $89715938 * $ and it is divisible by 4.
We are required to find the value of non – zero digit denoted by $\left( * \right)$.
We know that for a number to be divisible by 4, it should hold true for the property: A number (with 3 or more digits) is divisible by 4 if the number formed by the last two digits of the number is divisible by 4.
Now, we have the last two digits of this number as $8 * $. We will check every option by putting them in the place of $\left( * \right)$ to verify if the number obtained will be divisible by 4 or not.
Option (A): 2
The number formed by putting $\left( * \right) = 2$ will be $82$. We know that $82$ is not divisible by 4 and leaves a remainder 2.
Hence, option (A) is incorrect.
Option (B): 3
The number formed by putting $\left( * \right) = 3$ will be $83$ which is again not divisible by 4 and leaves a remainder 3. Hence, option (B) is incorrect.
Option (C): 4
The number formed by putting $\left( * \right) = 4$ will be $84$and it is divisible by 4 with 0 remainder.
Hence, option (C) is correct.
Option (D): 6
The number formed by putting $\left( * \right) = 6$ will be $86$ and it is indivisible by 4 and gives a remainder 2.
Hence, option (D) is incorrect.
Hence, option (C) is the correct answer.

Note: In this question, you may get confused in implementation of the property of divisibility by 4. You have to check each and every option since such questions can have multiple answers correct. You can show that the number is divisible by 4 or not by factorization method as well instead of dividing them and showing that they leave remainder.