# Q. 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?

a. 1 and 2 only

b. 2 and 3 only

c. 1 and 3 only

d. 1, 2 and 3

Correct Answer: d. 1, 2 and 3

#### Question from UPSC Prelims 2022 CSAT Paper

**Explanation : **

## P is a prime number and q is a composite number

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.