Question

What is the least value of $*$ so that the number $9274*5$ is divisible by $9$?

• A. $0$
• B. $3$
• C. $4$
• D. $9$

Answer 1

The correct option is A

$0$

Explanation for the correct option:

Correct option is (a) $0$

We know that A number is divisible by $9$, if the sum of its digits is divisible by $9$.

Here, the sum of the digits of the given number $9274*5$ is $9+2+7+4+5=27$, which is divisible by $9$. Thus, if we replace $*$ by $0$ then the given number $927405$ will also be divisible by $9$.

Hence, the least value of $*$ so that the number $9274*5$ is divisible by $9$ will be $0$.

Explanation for the incorrect options:

option (b) $3$

Here, the sum of the digits of the given number $9274*5$ is $9+2+7+4+5=27$, which is divisible by $9$. Thus, if we replace $*$ by $3$ then the given number $927435$ results the sum as $9+2+7+4+3+5=30$ which is not divisible by $9$.

option (c) $4$

Here, the sum of the digits of the given number $9274*5$ is $9+2+7+4+5=27$, which is divisible by $9$. Thus, if we replace $*$ by $4$ then the given number $927445$ results the sum as $9+2+7+4+4+5=31$ which is not divisible by $9$.

option (d) $9$

Here, the sum of the digits of the given number $9274*5$ is $9+2+7+4+5=27$, which is divisible by $9$. Thus, if we replace $*$ by $9$ then the given number $927495$ results the sum as $9+2+7+4+9+5=36$ which is divisible by $9$. But $9$ will be the greatest value for the given number.

Hence, the correct option is (a) $0$