CTET 2 Math and Science Dec 2019 Paper

Given, an 8-digit number 30x0867 is divisible by 88
∴ the number 30x0867y is divisible by 8 and 11
∵ A number is divisible by 8 if the number formed by hundred’s, ten’s and unit’s digit of the given number is divisible by 8
∴ 67y is divisible by 8
$\therefore \frac{67}{8}\mathit{y}=84$, when y = 2
And, a number is divisible by 11 if the difference between the sum of its digits at odd place and the sum of its digits of even place is either 0 or a number divisible by 11.
∴ (7 + 8 + x + 3) – (y + 6 + 0 + 0)
= 18 + x – (2 + 6)
= 18 + x – 8
= 10 + x
$\therefore \frac{10+\mathit{x}}{11}=1$, when x = 1
Therefore, (3x + y) = (3 × 1 + 2) = 3 + 2 = 5