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?

QUESTION

CSAT

Easy

Maths

Prelims 2023

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:

Which of the above statements is/are correct?

Select an option to attempt

Explanation

Among p. q, r, s, and t, there are three even and two odd numbers. Let the numbers be 2, 3, 4, 5 and 6.

Statement 1: $p + q + r – s - t$

No matter how we arrange the numbers, we always end up with an even number.

So, statement 1 is correct.

Statement 2: $2p + q + 2r – 2s + t$

Let’s put some values in this expression and check. $(2 \times 5) + 6 + (2 \times 3) – (2 \times 2) + 4 = 10 + 6 + 6 – 4 + 4 = 22$ (an even number)

So, statement 2 is incorrect.

Hence, option A is correct.

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