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# What does p equal?

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Manager
Joined: 15 Jan 2011
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What does p equal? [#permalink]  25 Jun 2012, 10:57
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Difficulty:

65% (hard)

Question Stats:

46% (02:14) correct 54% (01:08) wrong based on 81 sessions
What does p equal?

(1) $2p^2=p^3$

(2) $p=2\sqrt{p-1}$

i went with D, but was wrong

(1) 2p^2=p^3 divided by p^2 --> 2=p - here was the mistake and id like to ask you to shed the light on this - what don't i understand correctly here?
[Reveal] Spoiler: OA
Math Expert
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Kudos [?]: 40432 [2] , given: 5421

What does p equal? [#permalink]  25 Jun 2012, 11:07
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Expert's post
Galiya wrote:
What does p equal?

(1) 2p^2=p^3
(2) p=2sqrt{p-1}

i went with D, but was wrong

(1) 2p^2=p^3 divided by p^2 --> 2=p - here was the mistake and id like to ask you to shed the light on this - what don't i understand correctly here?

What does p equal?

(1) 2p^2=p^3 --> $p^3-2p^2=0$ --> $p^2(p-2)=0$ --> $p=0$ or $p=2$. Not sufficient.

(2) $p=2\sqrt{p-1}$ --> $p^2=4(p-1)$ --> $p^2-4p+4=0$ --> $(p-2)^2=0$ --> $p=2$. Sufficient.

As for your solution: you cannot divide by $p^2$ since $p$ could be zero and division by zero is not allowed.

Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero. So, if you divide (reduce) by $p^2$ you assume, with no ground for it, that $p$ does not equal to zero thus exclude a possible solution.

Hope it's clear.
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Manager
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Re: What does p equal? [#permalink]  25 Jun 2012, 11:14
thank you, Bunuel!sometimes Im really stuck on such a silly things
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Re: What does p equal? [#permalink]  30 Jun 2014, 06:39
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Re: What does p equal?   [#permalink] 30 Jun 2014, 06:39
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