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UPSC CSE 2024 · PYQ · Number Properties (Odd/Even) · easy

Let p, q, r and s be distinct positive integers. Let p, q be odd and r, s be even. Consider the following statements : 1. (p − r)²(qs) is even. 2. (q − s)q²s is even. 3. (q + r)²(p + s) is odd. Which of the statements given above are correct?

  1. A.1 and 2 only
  2. B.2 and 3 only
  3. C.1 and 3 only
  4. D.1, 2 and 3✓ Correct

Explanation

Statement 1: (p−r) is odd−even=odd, (p−r)² is odd; qs is odd×even=even; odd×even=even. Correct. Statement 2: (q−s) is odd−even=odd, q² is odd, s is even; odd×odd×even=even. Correct. Statement 3: (q+r) is odd+even=odd, (q+r)² is odd; (p+s) is odd+even=odd; odd×odd=odd. Correct. All three statements are correct.
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