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What does p equal?

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What does p equal? [#permalink] New post 25 Jun 2012, 10:57
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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
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What does p equal? [#permalink] New post 25 Jun 2012, 11:07
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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.

Answer: B.

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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Re: What does p equal? [#permalink] New post 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] New post 30 Jun 2014, 06:39
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What does p equal? [#permalink] New post 24 May 2015, 09:41
What does p equal?
1) 2p^2 = p^3
2) p = 2 sqrt (p-1)

Source: Optimus Prep

The way I thought about the first statement was to divide both sides by p^2; accordingly, I got p = 2. The explanation given, however, was as follows:
1. p^3 - 2p^2 = 0
2. p^2(p - 2) =0
3. p = 0 or p-2 =0
Therefore, p could be either 0 or 2.

Could anyone please explain why the way i went about the first statement was wrong? :?
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Re: What does p equal? [#permalink] New post 24 May 2015, 09:44
Expert's post
naeln wrote:
What does p equal?
1) 2p^2 = p^3
2) p = 2 sqrt (p-1)

Source: Optimus Prep

The way I thought about the first statement was to divide both sides by p^2; accordingly, I got p = 2. The explanation given, however, was as follows:
1. p^3 - 2p^2 = 0
2. p^2(p - 2) =0
3. p = 0 or p-2 =0
Therefore, p could be either 0 or 2.

Could anyone please explain why the way i went about the first statement was wrong? :?


Merging topics.

I think your doubt is addressed in my solution above.

Hope it helps.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: What does p equal? [#permalink] New post 24 May 2015, 10:23
Expert's post
Hi naeln,

You have to be careful when dividing by variables because you might accidentally REMOVE a potential solution to the equation.

Here's a simple example of that 'error':

How many solutions does the following equation have?

X^3 = X

Without too much trouble, you should realize that the solutions are...

[Reveal] Spoiler:
-1, 0 and 1


If you divide both sides by X though, you get....

X^2 = 1

Now the solutions are....

[Reveal] Spoiler:
-1 and 1. WHERE did the 0 go????? You divided it "out" when you divided both sides by X
.

Since each prompt requires that you properly deal with what you were given, you are responsible to find ALL of the potential answers. If you're thinking about dividing by a variable, then you might instead try factoring the equation first.

GMAT assassins aren't born, they're made,
Rich
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Re: What does p equal?   [#permalink] 24 May 2015, 10:23
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