Question

The number divisible by $11$ is:

• A. $11,11,111$
• B. $22,222$
• C. $3,33,33,333$
• D. $44,44,444$

Answer 1

The correct option is C

$3,33,33,333$

Explanation for the correct option:

Option (c) $3,33,33,333$

We know that A number is divisible by $11$, if the difference between the sum of digits at odd places and the sum of digits at even places is either $0$ or multiple of $11$.

Here, Sum of digits at odd places $=3+3+3+3=12$

And Sum of digits at even places $=3+3+3+3=12$

Since, the difference$=12–12=0$. Therefore, the given number is divisible by $11$.

Explanation for the incorrect options:

Option (a) $11,11,111$

We know that A number is divisible by $11$, if the difference between the sum of digits at odd places and the sum of digits at even places is either $0$ or multiple of $11$.

Here, Sum of digits at odd places $=1+1+1+1=4$

And Sum of digits at even places $=1+1+1=3$

Since, the difference$=4–3=1$. Therefore, the given number is not divisible by $11$.

Option (b) $22,222$

We know that A number is divisible by $11$, if the difference between the sum of digits at odd places and the sum of digits at even places is either $0$ or multiple of $11$.

Here, Sum of digits at odd places $=2+2+2=6$

And Sum of digits at even places $=2+2=4$

Since, the difference$=6–4=2$. Therefore, the given number is not divisible by $11$.

Option (d) $44,44,444$

We know that A number is divisible by $11$, if the difference between the sum of digits at odd places and the sum of digits at even places is either $0$ or multiple of $11$.

Here, Sum of digits at odd places $=4+4+4+4=16$

And Sum of digits at even places $=4+4+4=12$

Since, the difference$=16–14=2$. Therefore, the given number is not divisible by $11$.

Hence, the correct option is (c) $3,33,33,333$