39. 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)q^2 s is even.
3. (q + r)^2 (p + s) is odd.

Which of the statements given above are correct?

Question

Accepted Answer

The correct answer is option D. Given: p, q are odd integers; r, s are even integers.
1. (p - r)^2 (qs): (odd - even) = odd. So, (p - r)^2 = odd^2 = odd. (q × s) = (odd × even) = even. Therefore, (p - r)^2 (qs) = odd × even = even. Statement 1 is correct.
2. (q - s)q^2 s: (q - s) = (odd - even) = odd. q^2 = odd^2 = odd. s is even. Therefore, (q - s)q^2 s = odd × odd × even = even. Statement 2 is correct.
3. (q + r)^2 (p + s): (q + r) = (odd + even) = odd. So, (q + r)^2 = odd^2 = odd. (p + s) = (odd + even) = odd. Therefore, (q + r)^2 (p + s) = odd × odd = odd. Statement 3 is correct.
All three statements are correct. This question tests basic properties of odd and even numbers (parity) and their behavior under arithmetic operations.

Q39. 39. 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)q^2 s is even.
3. (q + r)^2 (p + s) is odd.

Which of the statements given above are correct?

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Q39. 39. 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)q^2 s is even.3. (q + r)^2 (p + s) is odd.Which of the statements given above are correct?

Detailed Solution

More Quantitative Aptitude Questions

More from UPSC 2024 CSAT

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Q39. 39. 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)q^2 s is even.
3. (q + r)^2 (p + s) is odd.

Which of the statements given above are correct?