kaplan DS question 2

dunkin77 wrote:If x and y are non-zero integers, what is the reminder when x is divided by y?

1) when x is divided by 2y, the remainder is 4.
2) when x + y is divided by y, the reminder is 4.

The answer is B but can anyone help?

Nice question.

1 - insufficient.
x = 2yt + 4 (where t is an integer)
x/y = 2t + 4/y

Now, depending on the value of y, we get remainder 4/y.
For example y=1 will give remainder 4, y=2 will give remainder 2 etc.

2 - sufficient. x + y and x are 'y' distance apart. y/y will give remainder
of zero. So, x+y and y will have the same remainder when divided
by y.

So, B