A question is given followed by two Statements I and II. Consider the Questions 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?

1. A. The question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
2. B. The Question can be answered by using either Statement alone
3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
4. D. The Question cannot be answered even by using both the Statements together

Answer: C

Explanation

We need to find unique distinct natural numbers x and y.

**Statement I: x/y is odd.**
Possible pairs (x,y) where x/y is an odd natural number:
– If y=1, x can be 3, 5, 7, … (e.g., (3,1), (5,1))
– If y=2, x can be 6, 10, 14, … (e.g., (6,2), (10,2))
Since there are multiple possibilities, Statement I alone is insufficient.

**Statement II: xy = 12.**
Possible pairs (x,y) of distinct natural numbers:
– (1,12), (2,6), (3,4), (4,3), (6,2), (12,1).
Since there are multiple possibilities, Statement II alone is insufficient.

**Combining Statement I and Statement II:**
We need a pair (x,y) from the list in Statement II where x/y is an odd natural number.
– (1,12): x/y = 1/12 (not an integer, so not odd)
– (2,6): x/y = 2/6 = 1/3 (not an integer)
– (3,4): x/y = 3/4 (not an integer)
– (4,3): x/y = 4/3 (not an integer)
– (6,2): x/y = 6/2 = 3 (which is an odd natural number). This gives (x=6, y=2).
– (12,1): x/y = 12/1 = 12 (which is an even natural number, not odd).

The only pair that satisfies both conditions is (6,2). Thus, x=6 and y=2 are uniquely determined.
Therefore, both statements together are sufficient. This question tests data sufficiency and number properties.