A question is given followed by two Statements I and II. Consider the Question and the Statements. Question:…
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?
The question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
The Question can be answered by using either Statement alone
The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
The Question cannot be answered even by using both the Statements together
Solution
Statement I alone: x/y being odd has many possibilities, not sufficient. Statement II alone: $xy = 12$ allows (12,1), (4,3), (6,2) - not sufficient. Combining: of these pairs, $12/1 = 12$ (not odd), $4/3$ (fraction), $6/2 = 3$ (odd). Only (6,2) satisfies both, giving unique values x = 6, y = 2. Hence both statements together are required.