Question

Which of the following numbers is divisible by $9$?
A) $863$
B) $932$
C) $752$
D) $837$

Answer 1

Hint: If a number is divisible by nine, the sum of the digits must also be divisible by nine. So we can check this point in each option. Thus we can find the right answer.

Complete step-by-step answer:
The given numbers are $863,932,752,837$.
We have to find which among this is divisible by $9$. Or simply which among this is a multiple of nine.
If a number is divisible by nine, the sum of the digits must also be divisible by nine.
So we can check each of the options.
A) $863$
We can see the sum of the digits is $8 + 6 + 3 = 17$. But $17$ is not a multiple of nine.
We have, $17 = 9 \times 1 + 8$
So A cannot be the answer.
B) $932$
We can see the sum of the digits is $9 + 3 + 2 = 15$. But $15$ is not a multiple of nine.
We have, $15 = 9 \times 1 + 6$
So B cannot be the answer.
C) $752$
We can see the sum of the digits is $7 + 5 + 2 = 14$. But $14$ is not a multiple of nine.
We have, $14 = 9 \times 1 + 5$
So C cannot be the answer.
D) $837$
We can see the sum of the digits is $8 + 3 + 7 = 18$. Also $18$ is a multiple of nine.
We have, $18 = 9 \times 2 + 0$
So D is the answer.

Option D is the correct answer.

Note: If a number $a$ is divisible by a number $b$, then we can write $a = bq + r$, where $r = 0$, that is $a = bq$, for some integer $q$.
If a number is divisible by 9 then it is divisible by 3 as well. But if a number is divisible by 3 then it may or may not be divisible by 9.