Prep question

zozo123 wrote:What is the remainder when the positive integer X is divided by 6 ?

1) When X is divided by 2, the remainder is 1; when X is divided by 3, the remainder is 0.

2) When X is divided by 12, the remainder is 3.


Do you have a strategy to slve this type of question ?

Plug in a few numbers to solve this problem quickly.

1 - sufficient. Skip even multiples of 3 as X is not divisible by 2.
Take x = 3, 9, 15 ... All of them yield a remainder of 3.

If you can see the pattern, X can be represented as 6t + 3, where t is
an integer. So, the remainder will always be 3.

2 - sufficient. Take x = 3, 15, 27, 39 ... again they all yield the same
remainder. Should be easy to see that the remainder (i.e. 3) and 6
don't have a common factor other than 3. So, dividing x by either 6 or
12 should give you the same remainder.

Thanks you Jayhawk!!