Question

If $5x6$ is divisible by 3, then the smallest possible value of $x$ is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is B 1

A number is divisible by 3 only when the sum of its digits is divisible by 3.
$5x6$ is divisible by 3. (given)
$\therefore$ Sum of its digits must be divisible by 3.
$\Rightarrow$ $5+x+6=11+x$ is divisible by 3.
The smallest multiple of 3 which is greater than 11 is 12.
$11+x=12\Rightarrow x=1$
$\therefore$ The smallest possible value of x will be 1.