Question

Choose the correct answer:

Which one of the following number is exactly divisible by $11$

• A. $235641$
• B. $245642$
• C. $315624$
• D. $415624$

Answer 1

The correct option is D

$415624$

Let's check the divisibility of each number.

If the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11 completely.

Option (A) $235641$

Here, the number of digits is $6$

So, $$\begin{gathered} \left(2+5+4\right)-\left(3+6+1\right) \\ =11-10=1 \end{gathered}$$

This number cannot be divisible by $11$

So, option (A) is wrong

Option (B) $245642$

So, $$\begin{gathered} \left(2+5+4\right)-\left(4+6+2\right) \\ =11-12 \\ =2 \end{gathered}$$

This number cannot be divisible by $11$

So, option (B) is wrong

Option (C) $315624$

So, $$\begin{gathered} \left(3+5+2\right)-(1+6+4) \\ =10-11 \\ =1 \end{gathered}$$

This number cannot be divisible by $11$

So, option (C) is wrong.

Option (D) $415624$

So, $$\begin{gathered} \left(4+5+2\right)-\left(1+6+4\right) \\ 11-11 \\ =0 \end{gathered}$$

This number can be divisible by $11$

Therefore, option (D) is correct