Question

if the number 362a349 where a is digit, is divisible by 11, the digit will be

option-
1). 1
2). 3
3). 6
4). 7​

Answer 1

According to the divisiblity rule of 11, it is said that a number is said to be divisible by 11 when the difference of the sum of the digits in its even places and the sum of the digits in the odd places of the number, is divisible by 11.

Thus, in this case

Odd placed digits of the number are 3, 2, 3, 9

Even placed digits of the number are 6, a, 4

On adding the odds we get

3 + 2 + 3 + 9 = 17

On adding the evens we get

10 + a

Now, their difference

17 - 10 + a

= 7 + a

Now, according to the rule

7 + a should be exactly divisible by 11.

Which means their quotient will be 0.

Thus the equation will be:

$\large { \frac{7 + a}{11} = 0}$

= $\large { 7 + a = 0}$ (sinec by transpositioning 11 we get 0— 11 × 0 = 0)

= $\large { a = -7}$

As a digit between a number can't be negative, hence the number has to be absolute.

Thus the absolute value of -7 is 7 which is the required number.

Thus, Option 4 is correct.

Bonus:

What is absolute value of a number?

→ It is the value of a number which shows how far is the given number from 0 in the number line, or in short it is the distance between the given number and 0 on the number line. Hence, it is never negative, but it is always positive, as in physics distance can never be negative but displacement can be negative.