Question

The number $12,375$ is
I. divisible by $3$.
II. divisible by $11$.
III. divisible by $9$.

Among the statements I, II and III,

• A. I, II and III are correct.
• B. I and II are correct.
• C. II and III correct.
• D. I and III are correct.

Answer 1

The correct option is A I, II and III are correct.

The number is $12375$
For divisibility by 3,
Sum of digits must be divisible by 3
$1+2+3+7+5=18$ which is divisible by 3.
For divisibility by 11,
Sum of digits at odd place - sum of digits at even must be equal to zero or divisible by 11.
$(1+3+5)-(2+7)=0$
Hence, it is divisible by 11.
For divisibility by 9
Sum of digits must be divisible by 9
$1+2+3+7+5=18$ which is divisible by 9.

Hence, $12375$ is divisible by 9.