Consider the following statements in respect of two natural numbers p and q such that p is a prime number and q is a composite number: 1. p x q can be an odd number. 2. q / p can be a prime number. 3. p + q can be a prime number. Which of the above statements are correct?

Let's analyze each statement:

1. p x q can be an odd number. For a product of two numbers to be odd, both numbers must be odd. Can p be an odd prime? Yes, for example, p = 3. Can q be an odd composite number? Yes, for example, q = 9 (which is 3x3). If p = 3 and q = 9, then p x q = 3 x 9 = 27, which is an odd number. So, statement 1 is correct.

2. q / p can be a prime number. Let p = 3 (a prime number). We need a composite number q such that q / 3 is a prime number. Consider q = 15. It is a composite number (3x5). Then q / p = 15 / 3 = 5, which is a prime number. So, statement 2 is correct.

3. p + q can be a prime number. Let p = 2 (a prime number). We need a composite number q such that p + q is a prime number. Consider q = 9. It is a composite number (3x3). Then p + q = 2 + 9 = 11, which is a prime number. So, statement 3 is correct.

Since all three statements are correct, the answer is D.