Three of the five positive integers p, q, r, s, t are even and two of them are odd (not necessarily in order). Consider the following :
1. p + q + r - s - t is definitely even.
2. 2p + q + 2r - 2s + t is definitely odd.

Which of the above statements is/are correct ?

Correct Answer: (A) 1 only

Among the five integers, 3 are even and 2 are odd, making their total sum $(p + q + r + s + t)$ an even number (since the sum of two odd numbers is even). In Statement 1, $p + q + r - s - t$$\equiv$ p + q + r + s + t \pmod 2, which is definitely even regardless of which variables are odd (Statement 1 is correct). In Statement 2, $2p + q + 2r - 2s + t$$\equiv$ q + t \pmod 2; if both $q$ and $t$ happen to be even (for instance, with odd integers being $s$ and $r$), then $q + t$ is even, so the expression is not definitely odd (Statement 2 is incorrect).