Let p, q, r and s be distinct positive integers. Let p, q be odd and r, s be even. Consider the following…
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. $(q-s)q^2s$ is even.
3. $(q+r)^2(p+s)$ is odd.
Which of the statements given above are correct?
1 and 2 only
2 and 3 only
1 and 3 only
1, 2 and 3
Solution
p, q are odd and r, s are even. Statement 1: $(p-r)^2(qs)$ is even because the factor s is even - correct. Statement 2: $(q-s)q^2s$ is even because s is even - correct. Statement 3: $(q+r)$ is odd and $(p+s)$ is odd, so $(q+r)^2(p+s)$ is odd x odd = odd - correct. Hence all three statements are correct.