CTET 2 Math and Science Jan 2021 Paper

If the number $179\mathit{x}091\mathit{y}$ is to be divided by 88 , then it must be divided by 8 and 11.
We know that if the difference between the sum of digits at even and odd position is divisible by 11 , then the number is also divisible by 11.
$\left(7+\mathit{x}+9+\mathit{y}\right)-\left(1+9+0+1\right)$ $=5+\mathit{x}+\mathit{y}$
To make $5+\mathit{x}+\mathit{y}$ divisible by 11 , $\mathit{x}+\mathit{y}$ must be equal to 6 . Now, we know that, if last three digits of a number is divisible by 8 , then the number is also divisible by 80.
Hence, if $\mathit{y}=2$, then 912 is exactly divisible by 8.
$\therefore \mathit{y}=2$ and $\mathit{x}=6-2=4$
$\Rightarrow \mathit{x}-\mathit{y}=4-2=2$