Question

X is a two - digit number. Y is the number obtained on reversing the digits of X. Which of the following is true?

• A. $X+Y$ is divisible by $10$
• B. $X-Y$ is divisible by $6$
• C. $X-Y$ is divisible by $9$
• D. $X+Y$ is divisible by $8$

Answer 1

Answer: (C)

$X-Y$ is divisible by $9$

Given: $X$ is two digit number

Let $X=10a+b$

$Y$ is number obtained by reversing digits of $X$

$\therefore Y=10b+a$

$X+Y=11(a+b)$ $\to$ divisible by $11$

$X-Y=9(a-b)$ $\to$ divisible by $9$