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# Is Q a prime number?

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Is Q a prime number? [#permalink]

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17 Jun 2010, 04:32
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Difficulty:

55% (hard)

Question Stats:

62% (03:17) correct 38% (01:20) wrong based on 55 sessions

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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]

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17 Jun 2010, 06:26
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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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Re: Is Q a prime number? [#permalink]

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17 Jun 2010, 07:32
Thanks Bunuel. This confirmed my reasoning.
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Re: Is Q a prime number? [#permalink]

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05 Jan 2017, 10:31
Bunuel wrote:
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.

"if $$q=4$$, then answer is NO". Is it correct or typing error?
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Kudos [?]: 105834 [0], given: 11589

Re: Is Q a prime number? [#permalink]

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05 Jan 2017, 10:36
Mahmud6 wrote:
Bunuel wrote:
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.

"if $$q=4$$, then answer is NO". Is it correct or typing error?

Why do you think it's an error? 4 + 2 = 6, which is not a prime, so the second statement is satisfied and 4 is not a prime, so the answer to the question whether q is a prime is no.
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Re: Is Q a prime number? [#permalink]

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05 Jan 2017, 10:55
Sorry, Bunuel.
My thought went in different ways, that's why I could not get it. You are right. Thanks.
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Re: Is Q a prime number?   [#permalink] 05 Jan 2017, 10:55
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