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?                                  

(UPSC CSAT – 2022)

1. 1 and 2 only
2. 2 and 3 only
3. 1 and 3 only
4. 1, 2 and 3

Solution: Ans.(d)

We can take some values of p and q according to question and check which statements is/are correct,

1. p × q = 7 × 9 = 63 (odd)

2. q ÷ p = 15 ÷ 3 = 5 (prime)

3. p + q = 5 + 6 = 11 (prime)

Hence, all three statements are correct.