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 Post subject: AlgebraPosted: Mon May 11, 2009 7:21 am

Joined: Tue Mar 17, 2009 11:38 am
Posts: 1
I'm working through the GMAT quant book and question 105 states that if you have:

z = (x^1/2) / (Y^1/2), then you can square both sides and get z^2 = x/y

I'm wondering how this is possibly since your not multiplying both sides by a two or a three, but by different variables.

Thanks!

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 Post subject: Re: AlgebraPosted: Fri May 15, 2009 5:10 pm

Joined: Fri May 15, 2009 4:59 pm
Posts: 4
One way to think about what's going on in this equation is that we multiply both sides of the original equation

1) z = (x^1/2) / (y^1/2)

by z. That gives us

2) z^2 = z * (x^1/2) / (y^1/2)

Now, we already know from statement (1) that z = (x^1/2) / (y^1/2), so we can rewrite the right side of the equation as follows:

3) z^2 = [ (x^1/2) / (y^1/2) ] * [ (x^1/2) / (y^1/2) ]

which simplifies to

4) z^2 = x^2 / y^2

Because the left and right side of the equation are equal, multiplying anything by 'z' will give the same result as multiplying by (x^1/2)/(y^1/2)

---

Your instinct is right when you say that multiplying by a constant has a different kind of effect than multiplying by a variable. For example, the equation

z = xy

returns the following when both sides are multiplied by 2:

2z = 2xy

This is relatively straightforward. But when we SQUARE both sides, what we're really doing is what I guided us through above:

1) z = xy

2a) z*z = xy * z

2b) z^2 = xyz AND z=xy [from statement 1]

3a) z^2 = xy(xy)

3b) z^2 = x^2y^2

---

So that's it. A little tricky to explain with ASCII, but hopefully that helps!

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