Question

What is the missing digit which makes the number $347\_$ exactly divisible by $11$?
1). $5$
2). $6$
3). $7$
4). $8$

Answer 1

Hint: First, we will know about the concept of the divisible by the number $11$, the difference of the sum of the alternate digits of a number is $0$ or a multiple of the number $11$ and then the number itself is a divisible of the number $11$
Example: take the number $19151$ and then sum of the odd digit numbers are $1 + 1 + 1$ (in the place of one, third and fifth) and the sum of the even digit numbers are $9 + 5$.
Thus to find its difference we have $3 - 14 = - 11$ which is exactly divisible by the number $11$ and hence the $19151$ is divisible by the number $11$

Complete step-by-step solution:
We will use the same concept which is given above to find the missing digit which makes the number $347\_$ exactly divisible by $11$
Since the sum of the odd digits are $3 + 7$ and the sum of the even digits are $4 + X$ (where X is the unknown value)
Hence the difference can be obtained as $3 + 7 - (4 + X)$ which divides the number $11$
Further solving we get $3 + 7 - (4 + X) = 10 - (4 + X)$
If the value of the X is six then we get the difference as zero and hence zero divides the number eleven.
Hence, we have $X = 6$ then we get $10 - (4 + 6) = 10 - 10 = 0$ and which divides the number $11$ (zero dividing all the numbers) thus number $3476$ exactly divisible by $11$
Therefore, the B) $6$ is correct.

Note: Note that if the value of the X is other than zero from $1,2,,,9$ then we did not get the difference which is divisible by the given number.
Take the value of X as $X = 1$ then we have the equation as $10 - (4 + 1) = 5$ clearly we see that the $5$ does not divide the number eleven and also which does not hold the divisible rule of eleven.
Hence the only possible number is six and which is the required answer.