Question

The number $7490xy$ is divisible by $90$. Find out the value of $(x+y)$.

• A. $4$
• B. $5$
• C. $6$
• D. $7$

Answer 1

The correct option is D $7$

$\Rightarrow$ $90=10\times 9$

$\Rightarrow$ $7490xy$ is divisible by 90. Since $10$ and $9$ are factors of $90$, $7490xy$ is divisible by $10$ and $7490xy$ is divisible by $9$.

$\Rightarrow$ $7490xy$ is divisible by $10$. We know that A number is divisible by $10$ if the last digit is $0$.

$\Rightarrow$ Hence $y=0$

$\Rightarrow$ Thus we have the number $7490x0$ which is divisible by 9.

$\Rightarrow$ sum of its digits of $7490x0$ is divisible by 9

$\Rightarrow$ $7+4+9+0+x+0$ is divisible by 9

$\Rightarrow$ $20+x$ is divisible by 9.

$\therefore$ $x=7$

$\Rightarrow$ $(x+y)=7+0=7$