Answer is D.
Solution, as follows:-
Statement 1st:
When x is divided by 2 , the reminder is 1 and when x is divided by 3 the reminder is 0.
So when x divides by 2 then reminder is 1. It means x is an odd +ive integer.
Also when x is divided by 3 then reminder is ZERO. It means x is an odd +ive multiple of 3.
It means x = 3, 9, 15, 21............
So now when x divided by 6, then reminder would always be 3.
Hence statement (1) can alone sufficient to derive the answer.
Now lets try with statement 2
Statement 2: When x is divided by 12, the reminder is 3.
To prove this statement, x should always be equal to (n * 12) + 3
i.e. x = (n *12) + 3, where n = 1, 2, 3...........
Now since (n * 12) would always be completely divisible by 6 no matter whatever the value of n is, so on dividing x by 6, the reminder would always be 3.
So statement (2) is alone sufficient to derive the answer.
As both statements are alone sufficient to derive the answer therefore IMO is (D)
