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Does p^2 = q if p is a prime number?

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Does p^2 = q if p is a prime number? [#permalink] New post 08 Apr 2012, 13:08
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Does p^2 = q if p is a prime number?

(1) q^2 - p^2 = 0
(2) p^2 = 49

I did not understand the OA.

From (1) - if p = 1, then q^2 = p^2 = p = +/-q
if p = 2, then p^2 = 4,p^2 is not equal to p. So (1) is not sufficient.
[Reveal] Spoiler: OA
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Re: Does p^2 = q if p is a prime number? [#permalink] New post 08 Apr 2012, 13:22
Expert's post
Does p^2 = q if p is a prime number?

Notice that we are told that p is a prime number.

(1) q^2 - p^2 = 0 --> p^2=q^2. Now, if p^2 = q is true, then from p^2=q^2 we would have that q=q^2 --> q(q-1)=0 --> q=0 or q=1, but in this case p becomes -1, 0, or 1, none of which is a prime number. Hence, p^2\neq{q}. Sufficient.

(2) p^2 = 49. Not sufficient as no info about q.

Answer: A.

Hope it's clear.
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Re: Does p^2 = q if p is a prime number? [#permalink] New post 14 Apr 2012, 10:29
I got this question wrong only because I thought the number 1 was prime, in that case A would have been insuffient. Let this be a lesson to you all. The number 1 is neither a prime nor a composite!! :)
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Re: Does p^2 = q if p is a prime number? [#permalink] New post 29 May 2013, 06:26
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Does p^2 = q if p is a prime number? [#permalink] New post 08 Jul 2014, 02:44
I approached this question as a YES/NO question.

Q: is p²=q? p is PRIME.

(1) q²-p²=0 , hence q²=p². This can only happen if q=1, -1 or 0, hence p also 1 or 0 which is no prime. Answer is NO, hence Suff.
(2) gives us no info about q, so IS.

Answer A.
Does p^2 = q if p is a prime number?   [#permalink] 08 Jul 2014, 02:44
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