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?

When we add or subtract even number of odd numbers, (ex – 7-3 or 5+7) we always get even number as answer. Also, doing addition & subtraction on even numbers always yields even number, so p + q + r – s – t will always be even.

Now, the problem with Statement 2 (2p + q + 2r – 2s + t) is that we don’t know how many of the two odd numbers are converted to even numbers by multiplying with 2. So, the resulting expression can be odd if there is only 1 odd number left.

So, statement 2 is incorrect. Hence, option (a) is the correct answer.