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

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Intern
Joined: 27 Sep 2010
Posts: 27

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

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22 Jan 2011, 01:07
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Difficulty:

85% (hard)

Question Stats:

48% (00:56) correct 52% (02:06) wrong based on 29 sessions

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

(1) (P – 1) (Q – 1) = 2
(2) P^2 + Q^2 = 13
[Reveal] Spoiler: OA

Kudos [?]: 87 [0], given: 3

Intern
Joined: 13 Oct 2010
Posts: 21

Kudos [?]: 8 [1], given: 0

Location: Milpitas, CA
Re: If P and Q are positive integers, is (P + 1)(Q + 1) = 12 ? [#permalink]

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22 Jan 2011, 01:47
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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:

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Kudos [?]: 8 [1], given: 0

Intern
Joined: 16 Jan 2011
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Kudos [?]: [0], given: 11

Re: If P and Q are positive integers, is (P + 1)(Q + 1) = 12 ? [#permalink]

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22 Jan 2011, 01:49
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

Kudos [?]: [0], given: 11

Intern
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Re: If P and Q are positive integers, is (P + 1)(Q + 1) = 12 ? [#permalink]

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22 Jan 2011, 02:00
Thank you!!

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Re: If P and Q are positive integers, is (P + 1)(Q + 1) = 12 ? [#permalink]

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30 Sep 2017, 09:20
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If P and Q are positive integers, is (P + 1)(Q + 1) = 12 ?   [#permalink] 30 Sep 2017, 09:20
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