Three positive integers a, b and c leave the same remainder y

Three positive integers a, b and c leave the same remainder y when divided by x, where x is a prime number greater than 3 and y is an integer greater than 1. What is the remainder when x is divided by y?

(1) c + 3 when divided by x yields an integer

(2) a + x - 2 when divided by x yields an integer

Pre-thinking on the question
x is an odd prime number
y is anything greater than 1.
Nothing much can be said from this information.

Considering Statement (1) alone:
Let c = 18, x = 7 => y = 4
So, when x is divided by y, the remainder is 3.

Let c = 12, x = 5 => y = 2
So, when x is divided by y, the remainder is 1.

INSUFFICIENT

Considering statement (2) alone:
Let a = 12, x = 5 => y = 2
So, when x is divided by y, the remainder is 1.

Let a = 5, x = 3 => y = 2
So, when x is divided by y, the remainder is 1.

Let a = 16, x = 7 => y = 2
So, when x is divided by y, the remainder is 1.

Clearly, the statement means that each of a, b, and c are 2 more than a multiple of x.
SUFFICIENT.

The answer is (B).