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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 × 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?

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 × 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? Correct Answer 1, 2 and 3

Option(4) is correct.

Statement 1: p × q can be an odd number: Correct if p and q both are odd then their product is odd. e.g., p = 3 and q = 15 then p × q = 45, which is a odd number.

Statement 2: q / p can be a prime number: Correct if composite number q is made of two prime numbers and p is one of that prime numbers then q/p is an odd number. e.g., p = 3 and q = 15 then q/p = 5, which is a prime number.

Statement 3: p + q can be a prime number: Correct if p = 5 and q = 6, then p + q = 11 which is a prime number.

Hence, the correct answer is an option(4) i.e.,1, 2, and 3.

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