UPSC CDS 2 2018 Math Paper

If a number is divisible by 33, then it is divisible by 11 as well as 3.
The number is divisible by 11. Therefore: 2X+Y–2X=11
⇒Y=0
The number is divisible by 3.
Therefore:
4X+Y=3k, where k is a positive integer
⇒4x=3k⇒X=

3

4

k
Since X is a positive integer, therefore, k will be a multiple of 4, i.e., 4, 8 or 12.
Note: K cannot be 16 or more as X is a single–digit number.
Therefore, X = 3, 6 or 9.
Hence, the possible numbers are 33033, 66066 and 99099.