Question

If the number $573xy$ is divisible by $90$, then what is the value of $x+y$ ?

Answer 1

573 xy is divisible by 90 i.e. (9 x 10)
$\Rightarrow$ 573 xy is divisible by both 9 and 10
$\Rightarrow$ y = 0 as a number is divisible by 10 if its ones' digit =0
Also sum of digits = 5 + 7 + 3 + x + 0 = 15 + x
For divisibility by 9, 15 + x = 18 $\Rightarrow$ x = 3
$\therefore$ x + y = 3 + 0 = 3