Data Sufficiency (DS) | If P and Q are positive integers, then is (P+2)(Q-1) an even number?

If P and Q are positive integers, then is (P+2)(Q-1) an even number?


(1)\(\frac{P}{3Q}\) is an even integer

P = Some Even integer * 3Q = Even Integer............Regardless of Q is even or odd.

Applying in question:

(P+2)(Q-1) = (Even+2)(Q-1) = Even * (Q-1) = Even

Sufficient

(2)\(\frac{Q}{\sqrt{P}-3}\) is a positive odd integer

Let Q=9 & P =16.........\(\frac{9}{\sqrt{16}-3}\) = 9

(16+2)(9-1) = Even..........Answer is Yes

Let Q = 2 & P =25.............\( \frac{2}{\sqrt{25}-3} \)
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