Consider the Question and two Statements given below:
- Question: Is x an integer?
- Statement–1: x/3 is not an integer.
- Statement–2: 3x is an integer.
Which one of the following is correct in respect of the Question and the Statements?
Answer & explanation
Answer: (d) Both Statement–1 and Statement–2 are not sufficient to answer the Question
x = 1 and x = 1/3 both satisfy both statements, but one is an integer and the other is not. So the statements cannot settle the question even when used together.
- Statement–1 alone: x = 1 gives x/3 = 1/3 (not an integer) and x is an integer; x = 1/2 gives x/3 = 1/6 and x is not an integer. Not sufficient.
- Statement–2 alone: x = 1 gives 3x = 3 and x = 1/3 gives 3x = 1; both are integers, yet only one x is an integer. Not sufficient.
- Together: x = 1 fits both (1/3 is not an integer, 3 is) and so does x = 1/3 (1/9 is not an integer, 1 is). One is an integer, the other is not.
- So even both statements together are not sufficient.
Remember · Data sufficiency: find two values that satisfy every statement yet give different answers — one such pair proves insufficiency.
Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·