Consider the following statements in respect of two natural numbers p and q such that p is a prime number and q is a composite number:
- 1.p × q can be an odd number.
- 2.q/p can be a prime number.
- 3.p + q can be a prime number.
Which of the above statements are correct?
Answer & explanation
Answer: (d) 1, 2 and 3
Each statement says ‘can be’, so one example is enough for each: 3 × 9 = 27 is odd, 6 ÷ 2 = 3 is prime, and 2 + 9 = 11 is prime. All three are correct.
- p = 3, q = 9: p × q = 27 is odd, so statement 1 is correct.
- p = 2, q = 6: q/p = 3 is prime, so statement 2 is correct.
- p = 2, q = 9: p + q = 11 is prime, so statement 3 is correct.
- All three statements are correct.
- ✓ 1. An odd prime times an odd composite is odd, e.g. 3 × 9 = 27.
- ✓ 2. e.g. 6 ÷ 2 = 3 (also 15 ÷ 5 = 3).
- ✓ 3. e.g. 2 + 9 = 11 (also 3 + 4 = 7).
Remember · ‘Can be’ statements need just one valid example; ‘must be’ statements need just one counter-example to fail.
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). ·