What does p equal?

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.

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...



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

X^2 = 1

Now the solutions are....

.

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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