If x denotes the digit at hundreds place of the number \(\overline{67

1.	If x denotes the digit at hundreds place of the number \(\overline{67\times19}\) such that the number is divisible by 11. Find all possible values of x.
Answer» Here, given number is \(\overline{67\times19}\) . We know that a number is divisible by 11 if and only if the difference between the sum of odd and even place digits is a multiple of 11. ∴ Sum of even placed digits – Sum of odd placed digits = 0, 11, 22,… ∴ (6 + x + 9) – ( 7+1) = 0, 11, 22,… ∴ x + 7 is a multiple of 11 ∴ x + 7 = 11 ∴ x = 4

If x denotes the digit at hundreds place of the number \(\overline{67\times19}\) such that the number is divisible by 11. Find all possible values of x.

Answer»

Here, given number is \(\overline{67\times19}\) .

We know that a number is divisible by 11 if and only if the difference between the sum of odd and even place digits is a multiple of 11.

∴ Sum of even placed digits – Sum of odd placed digits = 0, 11, 22,…

∴ (6 + x + 9) – ( 7+1) = 0, 11, 22,…

∴ x + 7 is a multiple of 11

∴ x + 7 = 11 ∴ x = 4