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UPSC PYQPrelims 2026

Civil Services Examination · Question 3

Each item contains a question followed by two statements. Answer using these instructions: (a) if the question can be answered using one of the statements alone, but cannot be answered using the other statement (b) if the question can be answered using either statement alone (c) if the question can be answered using both the statements together, but cannot be answered using either statement alone (d) if the question cannot be answered even using any of the statements Question: If x and y are integers, then is x even? Statement I: x²y² is even. Statement II: 1 + x² + y² is odd.

  1. Answerable using one statement alone, but not the other
  2. Answerable using either statement alone
  3. Answerable using both statements together, but not either alone
  4. Cannot be answered even using both statements
Show answer & explanation

Answer: (C) Answerable using both statements together, but not either alone

Explanation

I says at least one of x, y is even. II says x² + y² is even, so x and y have the same parity. Together both must be even, so x is even. Neither alone suffices.