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?

Since all statements say “can be”, we just need to find one case that is possible for each statement. This is not tough to do as shown below.

p is a prime number. So, p can be 2, 3, 5, 7, 11, 13, .….
q is a composite number. So, q can be 4, 6, 8, 9, 10, .….

Statement 1: p × q can be an odd number, e.g. (3 × 9 = 27). Thus, statement 1 is correct.
Statement 2: q/p can be a prime number, e.g. (4/2 = 2). Thus, statement 2 is correct.
Statement 3: p + q can be a prime number, e.g. (3 + 4 = 7). Thus, statement 3 is correct.

Thus, all the statements 1, 2 and 3 are correct.