We can substitute numbers to quickly figure this answer out.

With statement (1), 2 is a prime number, 4 is not. So not sufficient.

With statement (2), 3 is a prime number, 4 is not. So not sufficient.

Combined, with have something interesting. 2 is the only prime even number, and since we cannot include it, then all other even numbers we can think of will not be prime numbers. Regardless of whether x = 4, 6, 8, 10, 12, 14, 16, or 18, they'd all not be prime numbers. Hence together, statements (1) and (2) are sufficient. I.e. answer is C.

Another way to approach this question is to think back to the rules of prime numbers. Statement (1) cannot be sufficient because it includes both 2 and other even numbers, and we know 2 is a prime number while the others are not. Statement (2) include odd numbers, including a bunch that are definitely prime numbers, but also even numbers that are not. Combined, statement (2) actually only serves to rule out the number 2 as a possible even number for x. You don't and shouldn't even care about the fact that x has to be less than 19. The only time it'd matter is if x has to be < 4 or something, but that's not the case here, and I doubt would ever be the case in these sort of questions.

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Not a professional entity or a quant/verbal expert or anything. So take my answers with a grain of salt.