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# Is Q a prime number? 1) Q^2 - 2 = P; P is prime and P < 10

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Is Q a prime number? 1) Q^2 - 2 = P; P is prime and P < 10 [#permalink]  17 Jun 2010, 03:32
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Question Stats:

33% (07:02) correct 67% (00:36) wrong based on 3 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: DS - Prime number Q [#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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Joined: 24 Aug 2007
Posts: 956
WE 1: 3.5 yrs IT
WE 2: 2.5 yrs Retail chain
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Kudos [?]: 805 [0], given: 40

Re: DS - Prime number Q [#permalink]  17 Jun 2010, 06:32
Thanks Bunuel. This confirmed my reasoning.
Re: DS - Prime number Q   [#permalink] 17 Jun 2010, 06:32
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