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

Statement 1: $p \times q$ can be an odd number. For example, let $p = 3$ (prime) and $q = 9$ (composite). $p \times q = 3 \times 9 = 27$, which is an odd number. Hence, statement 1 is correct.

Statement 2: $q / p$ can be a prime number. For example, let $p = 2$ (prime) and $q = 4$ (composite). $q / p = 4 / 2 = 2$, which is a prime number. Hence, statement 2 is correct.

Statement 3: $p + q$ can be a prime number. For example, let $p = 3$ (prime) and $q = 4$ (composite). $p + q = 3 + 4 = 7$, which is a prime number. Hence, statement 3 is correct.

Since all three statements hold true in at least one case, all the statements 1, 2, and 3 are correct.