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?

(UPSC CSAT – 2023)

1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2

Solution: Ans.(1)

Statement 1.  If we add or subtract three even integers it results even number always. And if we add or subtract two odd integers it results even number always.

Therefore ( p + q + r – s – t ) is definitely even.

Statement 2.  In (2p + q + 2r – 2s + t), (2p + 2r – 2s) is always even number and (q + t) may be even or odd as per the value of q and t (even or odd)

Therefore (2p + q + 2r – 2s + t) may be even or odd.