What is the source of this question? This is not a GMAT-like question at all, for the following reasons:

- the GMAT will not use the term "natural number"

- because you do not have a calculator, you will not be expected to do laborious calculations such as 1098/18

- a correct answer on a DS question will ALWAYS make use of the given information. Here, statement 2 answers the question "is p divisible by 18" without in any way using the given information that p = rq - 289

To answer your question,

Below is the explanation they gave but the only reasoning for B being sufficient to them is they quoted "possible" Aren't DS questions based on either it solves the problem or Not. Not "possibility"

This explanation is just poorly worded. In fact, statement 2 PROVES that p is divisible by 18. Because of the rule that a multiple of a given integer n puls or minus another multiple of n will equal a multiple of n, if p minus a multiple of 18 = a multiple of 18, then p itself must be a multiple of 18.

This is clearly a very poor source for GMAT practice material. I'd recommend that you stop using it.