QUESTION

CSAT

Easy

Maths

Prelims 2023

Questions: Is (p+qr)(p + q - r) greater than (pq+r)(p - q + r), where p, q and r are integers? Statement-1: (pq)(p - q) is positive. Statement-2: (pr)(p - r) is negative.

Which one of the following is correct in respect of the above Question and the Statements?

Select an option to attempt

Explanation

Statement 1: (pq)(p - q) is positive. This is possible only when p>qp > q

Statement 2: (pr)(p - r) is negative. This is possible only when p<rp < r

Now, (p+qr)(pq+r)=2q2r(p + q - r) – (p – q + r) = 2q – 2r So, we basically need to find out if q>rq > r, or not. For this, we obviously have to use both the given statements.

Using both of the statements, we get: r>p>qr > p > q So, q<rq < r

It means that, (p+qr)(pq+r)=2q2r<0(p + q - r) – (p – q + r) = 2q – 2r < 0 In other words, (p+qr)(p + q - r) is not greater than (pq+r)(p – q + r).

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