Divisibilty q taken from dferm's post

[amitansu]

What is the reminder when positive integer x is divided by 6 ?

1. When x is divided by 2 , the reminder is 1 and when x is divided by 3 the reminder is 0.
2. When x is divided by 12, the reminder is 3.

My choice is E.

Any more explanations/views !!

[codesnooker]

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)

[amitansu]

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'?