ashikaverma13 wrote:

If p, q and r are integers, and pq + r is an odd integer, is p an even integer?

(1) pq + pr is an even integer.

(2) p + qr is an odd integer.

Given \(pq+r=Odd\)

Statement 1: \(pq+pr=Even\), add \(r\) to both sides

\(pq+r+pr=Even+r => Odd+pr=Even+r\)

or \(pr-r=Even-Odd => r(p-1)=Odd\)

\(1\) is odd so \(p\) has to be even because if \(p\) is odd then \(p-1\) is even and \(r(p-1)\) will be even which is not possible.

SufficientStatement 2: \(p+qr=Odd\)

so if \(p=even\) & \(r=Odd\) or \(p=odd\), \(q=odd\) and \(r=even\). So no unique solution.

InsufficientOption

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Another method. Plug in some values and test