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)

Once i concluded that both are sufficient to answer this q, i got confused seeing that 3/6 leaves a fraction.... evEn though 3=6*0+3 where 3 is reminder.

Basically i put this q to get rid of my 'confusion of whether 3/6 is fraction or leaves a reminder of 3'?