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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.
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Re: Does p^2 = q if p is a prime number? [#permalink] New post 08 Apr 2012, 13:22
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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.
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Re: Does p^2 = q if p is a prime number? [#permalink] New post 05 Sep 2015, 05:26
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Does p^2 = q if p is a prime number? [#permalink] New post 05 Sep 2015, 22:02
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Forget conventional ways of solving math questions. In DS, Variable approach is

the easiest and quickest way to find the answer without actually solving the

problem. Remember equal number of variables and equations ensures a solution.


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

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

according to variable approach method, since we have 2 variables (p,q) in the original condition we need 2 more to match the number of variables and equations. we have 1 each in 1) and 2), therefore C is likely the answer. Using both 1) & 2) together we have p=7, q=-7,7 and since no is the answer for p^2=49=7,-7, the condition is sufficient and the answer is C. but since the case if trivial, using common mistake type 4(A) we have 1) p^2=q^2 means q^2=q?, therefore q=0,1?. then we get p^2=0,1? and p=-1,0,1? and thus p is not a prime number, with answer as no. Therefore the condition is sufficient and the answer is A.
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Does p^2 = q if p is a prime number?   [#permalink] 05 Sep 2015, 22:02
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