A Question is given followed by two Statements I and II. Consider the Question and the Statements.
- Question: Is (x + y) an integer?
- Statement–I: (2x + y) is an integer.
- Statement–II: (x + 2y) is an integer.
Which one of the following is correct in respect of the above Question and the Statements?
Answer & explanation
Answer: (d) The Question cannot be answered even by using both the Statements together
Neither statement alone fixes x + y. Even together they only make 3(x + y) an integer, so x + y can be a fraction such as 2/3 (x = y = 1/3) or an integer (x = y = 1).
- Statement I alone: x = 0.5, y = 0 gives 2x + y = 1 but x + y = 0.5; x = y = 1 gives x + y = 2. Not sufficient.
- Statement II alone: the same examples with x and y swapped show it is not sufficient.
- Together: adding them, 3x + 3y is an integer, so x + y is only known to be an integer divided by 3.
- x = y = 1/3 gives 2x + y = 1 and x + 2y = 1, yet x + y = 2/3; x = y = 1 gives x + y = 2. Both fit, so the answer is still open.
Remember · In ‘is it an integer?’ questions, try fractions like 1/3 or 1/2; they often break an apparent ‘yes’.
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). ·