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# Q is less than 10. Is Q a prime number?

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Q is less than 10. Is Q a prime number?  [#permalink]

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17 Jun 2010, 03:32
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Difficulty:

65% (hard)

Question Stats:

66% (02:20) correct 34% (01:50) wrong based on 92 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.

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Re: Q is less than 10. Is Q a prime number?  [#permalink]

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17 Jun 2010, 05:26
1
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: Q is less than 10. Is Q a prime number?  [#permalink]

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17 Jun 2010, 06:32
Thanks Bunuel. This confirmed my reasoning.
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Re: Q is less than 10. Is Q a prime number?  [#permalink]

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05 Jan 2017, 09:31
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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Hasan Mahmud

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Re: Q is less than 10. Is Q a prime number?  [#permalink]

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05 Jan 2017, 09:36
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: Q is less than 10. Is Q a prime number?  [#permalink]

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05 Jan 2017, 09:55
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: Q is less than 10. Is Q a prime number?  [#permalink]

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27 Nov 2017, 11:25
1
Hi All,

We're told that Q is less than 10. We're asked if Q is a PRIME number. This is a YES/NO question.

1) Q^2 - 2 = P; P is prime and P < 10.

The information in Fact 1 severely limits the possible values of P (which will limit the possible values of Q. Since P is PRIME and P < 10....
P can be 2, 3, 5 or 7
By extension, Q could be +2, - 2, +√5, -√5, +√7, -√7, +3 or -3
IF...
Q=2 or 3, then the answer to the question is YES.
Q = any of the other values, then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) Q + 2 is NOT prime, but Q is a positive integer.

The information in Fact 2 limits the possible values of Q to the following: 2, 4, 6, 7 or 8
IF...
Q = 2 or 7, then the answer to the question is YES.
Q = 4, 6 or 8, then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, there's ONLY ONE value that 'fits' both Facts (Q=2)
Combined, SUFFICIENT

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Re: Q is less than 10. Is Q a prime number?   [#permalink] 27 Nov 2017, 11:25
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