Question

If a 4-digit number 4XY2 is exactly divisible by 3, then find the least value of (X + Y)?
(Note: X + Y cannot be zero)
$\left[3\right]$

Answer 1

If the 4-digit number 4XY2 is divisible by 3, then the sum of its digits will be divisible by 3.
$\left[1\right]$

4 + X + Y + 2 = 6 + X + Y
6 is divisible by 3 already.
$\left[1\right]$

So, to make 6 + X + Y divisible by 3, X + Y should also be divisible by 3.
So, the least value X + Y can take is 3.
$\left[1\right]$