UPSC CDS 2 2018 Math Paper

A number is divisible by 3 when the sum of its digits is divisible by 3.
Here sum of digitsAlso X+Y≤5
Since the number is a multiple of 3, therefore, (X + Y) can either be 2 or 5
Possible pairs of (X, Y) are (1, 1), (2,0), (1, 4), (2, 3), (3, 2), (4, 1), (5, 0)
Thus, 7 such pairs exist.