Question

If $AB$ is divisible by $5$ but not divisible by $2$ and $BA$ is divisible $3$, then which of the following is the possible value of $A$ and $B$?

• A. (x-2)(x-5)= – 7x + 10
• B. (x+2) (x-2) = - 4
• C. $A=7,B=5$
• D. $A=4,B=0$

Answer 1

The correct option is B

(x+2) (x-2) = - 4

Since, $AB$ is divisible by $5$, $B$ should be either $0$ or $5$. But since $AB$ is not divisible by $2$, $B$ is surely $5$.
Since, $BA$ is divisible by $3$, $A+B$ should also be divisible by $3$.
But $B$ is $5$. Thus, $A+5$ should also be divisible by $3$.
Among the options, $A+5$ will be divisible by $3$ only if $A=4$.