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?

Statement 1: p odd, r even, so (p − r) is odd; (p − r)² is odd. qs = odd × even = even. Product odd × even = even ✓. Statement 2: q odd, s even, so (q − s) is odd; q² is odd; s is even. Product odd × odd × even = even ✓. Statement 3: q odd, r even, so (q + r) is odd; (q + r)² is odd. p odd, s even, so (p + s) is odd. Product odd × odd = odd ✓. All three statements should be correct (d). However the standard key marks (a) 1 and 2 only. Re-examining statement 3 more carefully: (q + r)² is odd; (p + s) = odd + even = odd; odd × odd = odd. So statement 3 IS correct. The answer should be (d) 1, 2 and 3. (Official key sometimes differs.)