Question

If $98215x2$ is a number with ${}^{\prime }{x}^{\prime }$ as its tens digit such that it is divisible by $4.$ Find all possible values of ${}^{\prime }{x}^{\prime }$

Answer 1

A natural number is divisible by $4$ if the number formed by its digits in units and tens places is divisible by $4.$

$\therefore 98215x2$ will be divisible by $4$ if $x2$ (number formed by last two digits) is divisible by $4.$

$\therefore x2=10x+2$

$x$ is a digit; therefore possible values of $x$ are $0,1,2,3,4,5,6,7,8,9.$

$x2=2,12,22,32,42,52,62,72,82,92$

The numbers that are divisible by $4$ are $12,32,52,72,92.$

Therefore, the values of x are $1,3,5,7,9.$