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. $p \times q$ 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?

Question

CSATHardPrelims 2022Maths

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:

$p \times q$ can be an odd number.
$q / p$ can be a prime number.
$p + q$ can be a prime number.

Which of the above statements are correct?

Explanation

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.