Question

The 4-digit number $7x86$ is evenly divisible by 9 and other 4-digit number $7y86$ is evenly divisible by 3.
Which of the following are smallest values of $x\&y?$

• A. $x=6\&y=3$
• B. $x=3\&y=0$
• C. $x=6\&y=0$

Answer 1

The correct option is C $x=6\&y=0$

We know: If the sum of digits of a number is a multiple of 9, then the number is divisible by 9.

Given: $7x86$ is divisible by 9 that means its sum of digit $7+x+8+6=21+x$ is multiple of 9.
Here, smallest value of $x$ for which $21+x$ will be multiple of 9 is 6.$\Rightarrow 21+6=27$ is multiple of 9.


We know: If the sum of digits of a number is a multiple of 3, then the number is divisible by 3.

Given: $7y86$ is divisible by 3 that means its sum of digit $7+y+8+6=21+x$ is multiple of 3.
Here, smallest value of $y$ for which $21+y$ will be multiple of 3 is 0.$\Rightarrow 21+0=21$ is multiple of 3.