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.
