For what value of digit x is :

5x2 a multiple of 11 ?

According to the divisibility of 11, if the difference between the sum of its digits in even places and the sum of its digits in odd places is either 0 or divisible by 11 then the number is divisible by 11.

∴ 5x2 is divisible by 11
⇒ Sum of the digits in even place = x

Sum of the digits in odd place = 5 + 2 = 7

Difference between the sum of the digits in odd places and the sum of the digits in even places = 7 - x

⇒ 7 - x must be divisible by 11

⇒ 7 - x = 0, 11, 22, 33, ……………

⇒ x = 7, -4, -15, -26, ……………

Since x is a digit. So, x = 7.