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. px qcan be an odd number. 2. q / p can be a prime number. 3. p+ qcan be a prime number. Which of the above statements are correct?

The question asks which of the given statements about a prime number 'p' and a composite number 'q' are correct.

Let's analyze each statement:

1. p x q can be an odd number. For the product of two numbers to be odd, both numbers must be odd. Can 'p' be an odd prime? Yes, for example, p = 3, 5, 7, etc. (all primes except 2 are odd). Can 'q' be an odd composite number? Yes, for example, q = 9 (3x3), 15 (3x5), 21 (3x7), 25 (5x5). If p = 3 and q = 9, then p x q = 3 x 9 = 27, which is an odd number. So, statement 1 is correct.

2. q / p can be a prime number. 'q' is a composite number, and 'p' is a prime number. For q / p to be a prime number, 'q' must be a multiple of 'p', and the result must be prime. Let p = 3 (a prime number). Let q = 15 (a composite number, 3x5). Then q / p = 15 / 3 = 5, which is a prime number. Another example: Let p = 2 (a prime number). Let q = 6 (a composite number, 2x3). Then q / p = 6 / 2 = 3, which is a prime number. So, statement 2 is correct.

3. p + q can be a prime number. 'p' is a prime number, and 'q' is a composite number. We need to find if their sum can be prime. Let p = 2 (a prime number). Let q = 9 (a composite number). Then p + q = 2 + 9 = 11, which is a prime number. Another example: Let p = 3 (a prime number). Let q = 4 (a composite number). Then p + q = 3 + 4 = 7, which is a prime number. So, statement 3 is correct.

Since all three statements are correct, the answer is D.

The final answer is D