A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question:
What are the unique values of x and y, where x, y are distinct natural numbers?

Statement-I: x / y is odd.

Statement-II: xy = 12

Which one of the following is correct in respect of the above Question and the Statements?

Correct Option: (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone

We need to determine the unique values of distinct natural numbers x and y. From Statement-I: x / y is odd. This can be satisfied by infinitely many pairs of distinct natural numbers, such as (3, 1), (6, 2), or (15, 3). Thus, Statement-I alone is insufficient. From Statement-II: xy = 12. Since x and y are distinct natural numbers, the possible factor pairs for (x, y) are (1, 12), (2, 6), (3, 4), (4, 3), (6, 2), and (12, 1). Thus, Statement-II alone is insufficient. Combining both statements together: We must find a pair from the factors of 12 where x/y is an odd integer. Let us test the pairs: For (1, 12): 1/12 is not an integer. For (2, 6): 2/6 = 1/3 is not an integer. For (3, 4): 3/4 is not an integer. For (4, 3): 4/3 is not an integer. For (6, 2): 6/2 = 3, which is an odd integer. For (12, 1): 12/1 = 12, which is an even integer. The only pair satisfying both statements is x = 6, y = 2. Thus, both statements together uniquely determine the values. Hence, the correct option is (c).