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

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Intern
Joined: 14 Sep 2016
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If P and Q are positive integers, then is (P+2)(Q-1) an even number?  [#permalink]

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24 Jul 2017, 03:20
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45% (medium)

Question Stats:

62% (01:30) correct 38% (04:23) wrong based on 13 sessions

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

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

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

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24 Jul 2017, 03:41
1
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

Let Q = 2 & P =25............. $$\frac{2}{\sqrt{25}-3}$$= 1

Insufficient

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Re: If P and Q are positive integers, then is (P+2)(Q-1) an even number?  [#permalink]

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24 Jul 2017, 22:00
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 = Even integer * 3Q = Even
(P+2)(Q-1) =(Even +2 ) (Q-1)
P+2 will be even
Sufficient

(2) $$\frac{Q}{\sqrt{P}-3}$$ is a positive odd integer
If P=16 and Q=3 ,
$$\frac{Q}{\sqrt{P}-3}$$ = 3/1 = 3
=> (P+2)(Q-1) = even

If P = 25 and Q= 2
$$\frac{Q}{\sqrt{P}-3}$$ = 2/2 = 1
=> (P+2)(Q-1) = Odd
Not sufficient

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: If P and Q are positive integers, then is (P+2)(Q-1) an even number?   [#permalink] 24 Jul 2017, 22:00
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