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?
Answer & explanation
Answer: (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
‘x/y is odd’ alone allows endless pairs, and xy = 12 alone allows six ordered pairs. Together, of the pairs with product 12, only x = 6, y = 2 gives an odd quotient (3).
- Statement I alone: x = 3y, 5y, 7y, …, for example (3, 1), (5, 1), (6, 2); not unique.
- Statement II alone: (1, 12), (2, 6), (3, 4), (4, 3), (6, 2), (12, 1); not unique.
- Together, test x/y for each pair: 12/1 = 12 (even), 6/2 = 3 (odd); 4/3, 3/4, 2/6 and 1/12 are not whole numbers.
- Only x = 6, y = 2 works, so both statements together answer the question.
Remember · When one statement gives a short list, test each item on it against the other statement.
Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·