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If P and Q are positive integers, is (P + 1)(Q + 1) = 12?

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If P and Q are positive integers, is (P + 1)(Q + 1) = 12? [#permalink] New post 22 Jan 2011, 00:07
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Q) If P and Q are positive integers, is (P + 1)(Q + 1) = 12 ?
(1) (P – 1) (Q – 1) = 2
(2) P2+ Q2 = 13



Please explain...
[Reveal] Spoiler: OA
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Re: Is (P + 1)(Q + 1) = 12 ? [#permalink] New post 22 Jan 2011, 00:47
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MichelleSavina wrote:
If P and Q are positive integers, is (P + 1)(Q + 1) = 12 ?
(1) (P – 1) (Q – 1) = 2
(2) P2+ Q2 = 13


Statement 1: (P – 1)(Q – 1) = 2
2 has only two factors, 1 and 2.
Hence, either {(P - 1) = 1 and (Q - 1) = 2} or {(P - 1) = 2 and (Q - 1) = 1}
Thus, either {P = 2 and Q = 3} or {P = 3 and Q = 2}
In any case, (P + 1)(Q + 1) = 3*4 = 12

Sufficient

Statement 2: P² + Q² = 13
Only possible way to express 13 as a sum of two perfect squares is 13 = (2² + 3²)
Thus, either {P = 2 and Q = 3} or {P = 3 and Q = 2}
In any case, (P + 1)(Q + 1) = 3*4 = 12

Sufficient

[Reveal] Spoiler:
The correct answer is D.

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Re: Is (P + 1)(Q + 1) = 12 ? [#permalink] New post 22 Jan 2011, 00:49
Hi,
Simplifying the question 'Is (P+1)(Q+1)=12'. In simple terms it is asking us to determine the values of P and Q.
1.(P-1)(Q-1)=2. Possible combination of P and Q are (3,2) or (2,3). Both of which yield 12. Hence sufficient.
2.P2+Q2=13.Possible combination of P and Q are (3,2) or (2,3). Both of which yield 12. Hence sufficient.

Hence D
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Re: Is (P + 1)(Q + 1) = 12 ? [#permalink] New post 22 Jan 2011, 01:00
Thank you!! :)
Re: Is (P + 1)(Q + 1) = 12 ?   [#permalink] 22 Jan 2011, 01:00
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If P and Q are positive integers, is (P + 1)(Q + 1) = 12?

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