Question

1x98 is divisible by 11 then
what is value of x?​

Answer 1

The value of x = 2

Given :

1x98 is divisible by 11

To find :

The value of x

Concept :

Divisibility rule of 11:

A number is divisible by 11 if the sum of the digits in the odd places and the sum of the digits in the even places difference is a multiple of 11 or zero.

Solution :

Step 1 of 2 :

Calculate the sum of the digits in odd places and the sum of the digits in even places

Here the given number is 1x98

Now ,

The sum of the digits in odd places

= (1 + 9)

= 10

The sum of the digits in even places

= (x + 8)

Step 2 of 2 :

Find the value of x

Divisibility rule of 11 states that a number is divisible by 11 if the sum of the digits in the odd places and the sum of the digits in the even places difference is a multiple of 11 or zero.

(The sum of the digits in odd places) - (The sum of the digits in even places)

= 10 - (x + 8)

= 10 - x - 8

= 2 - x

Since 1x98 is divisible by 11

∴ 2 - x is either 0 or multiple of 11

Since x is a digit

This holds only if x = 2

Hence the required value of x = 2

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