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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]

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08 Apr 2012, 14:08
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Does p^2 = q if p is a prime number?

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

[Reveal] Spoiler:
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

Last edited by Engr2012 on 26 Apr 2016, 07:26, edited 1 time in total.
Reformatted the question.
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Re: Does p^2 = q if p is a prime number? [#permalink]

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08 Apr 2012, 14:22
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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 $$q$$.

Hope it's clear.
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Re: Does p^2 = q if p is a prime number? [#permalink]

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14 Apr 2012, 11:29
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]

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29 May 2013, 07:26
Expert's post
Bumping for review and further discussion.
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Re: Does p^2 = q if p is a prime number? [#permalink]

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08 Jul 2014, 03:44
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.

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Re: Does p^2 = q if p is a prime number? [#permalink]

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05 Sep 2015, 06:26
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Does p^2 = q if p is a prime number? [#permalink]

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05 Sep 2015, 23:02
Expert's post
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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Re: Does p^2 = q if p is a prime number? [#permalink]

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26 Apr 2016, 07:16
If the question stem states that $$p^2=q$$ does it not infer that 49=q in 2nd statement?
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Re: Does p^2 = q if p is a prime number? [#permalink]

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26 Apr 2016, 07:18
Expert's post
maipenrai wrote:
If the question stem states that $$p^2=q$$ does it not infer that 49=q in 2nd statement?

The stem does not say that p^2 = q, it asks about it: Does p^2 = q if p is a prime number?
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Re: Does p^2 = q if p is a prime number? [#permalink]

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26 Apr 2016, 07:29
Bunuel wrote:
maipenrai wrote:
If the question stem states that $$p^2=q$$ does it not infer that 49=q in 2nd statement?

The stem does not say that p^2 = q, it asks about it: Does p^2 = q if p is a prime number?

That's right.
I guess it is time for me to go to bed

Need to be more accurate at reading the questions.
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Re: Does p^2 = q if p is a prime number? [#permalink]

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26 Apr 2016, 07:45
p is prime. Is p^2 = q?

St1: p^2 - q^2 = 0
(p + q)(p - q) = 0
p + q = 0 or p - q = 0
p = -q or p = q
p is prime --> p can't be negative --> Only valid answer is p = q.
Primes are > 1. So if p = q then $$p^2 \neq {q}$$
Sufficient

St2: p^2 = 49 --> p = 7 --> Clearly insufficient as no information is provided about q

Re: Does p^2 = q if p is a prime number?   [#permalink] 26 Apr 2016, 07:45
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