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# Is Q a prime number?

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Is Q a prime number? [#permalink]  17 Jun 2010, 03:32
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Question Stats:

33% (05:42) correct 67% (01:17) wrong based on 6 sessions
Q is less than 10. Is Q a prime number?

(1) Q^2 - 2 = P; P is prime and P < 10.
(2) Q + 2 is NOT prime, but Q is a positive integer.
[Reveal] Spoiler: OA

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Re: Is Q a prime number? [#permalink]  17 Jun 2010, 05:26
Expert's post
ykaiim wrote:
Q is less than 10. Is Q a prime number?

1) $$Q^2$$ - 2 = P; P is prime and P < 10.
2) Q + 2 is NOT prime, but Q is a positive integer.

Given: $$q<10$$. Question: $$q=prime$$?

(1) $$q^2-2=p=prime<10$$ --> if $$p=7$$, then $$q=3=prime$$ or $$q=-3\neq{prime}$$. Not sufficient.

(2) $$q+2\neq{prime}$$, $$q=positive \ integer$$. If $$q=2$$ then answer is YES but if $$q=4$$, then answer is NO. Not sufficient. From this statement $$q$$ can take the following values: 2, 4, 6, 7, 8 (remember $$q<10$$ and $$q+2\neq{prime}$$).

(1)+(2) The only value from (2) that satisfies $$q^2-2=prime<10$$ is when $$q=2=prime$$. Sufficient.

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Director
Joined: 24 Aug 2007
Posts: 954
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
Followers: 59

Kudos [?]: 869 [0], given: 40

Re: Is Q a prime number? [#permalink]  17 Jun 2010, 06:32
Thanks Bunuel. This confirmed my reasoning.
Re: Is Q a prime number?   [#permalink] 17 Jun 2010, 06:32
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