What is this number? if I divide it by 2, the remainder is 1. If I divide by 3, the remainder is 2.

It can be anything.  You know it cannot be a even number, as if it is divided by 2 , then there would be no remainder, so it must be a odd no.  Also, it is not divisible by 3 like 3,6,9,12,15,18..... as it also won't have a remainder or also by 2 as it would not abide with the conditions stated above, {remainders when divisible by 2 and 3}.

The odd numbers are here: 3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37 and so on.

From this list, cancel out those that are multiples of 3.

So, 3,9,15,18,21,27,33 are all out

To test out the rest of the numbers fulfil those conditions:

5= 2R1, 1R2 (passed)

7= 3R1, 2R1 (failed)

11= 5R1, 3r2 (passed) and so. You should know by then which are the odd one out.