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Simple equation on GMAT (help me)

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Simple equation on GMAT (help me) [#permalink]

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New post 09 Nov 2015, 04:21
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Guys, can you help me with this simple question about factoring an equation ?

A question on quantitative part in OG 2016 ask to solve Y in terms of X. The equation is X^2.Y^2 - X.Y = 6

I already know how to find de answer. What I would like to know is why the first step that I did wasn't correct. This was my first step to find the solution:

X^2.Y^2 - X.Y = 6
X.Y(X.Y - 1) -6 = 0
X.Y - 6 =0
X.Y = 6
Y = 6/X

X.Y(X.Y - 1) -6 = 0
X.Y - 1 = 0
X.Y = 1
Y = 1/X

I know that the factorization in the equation ( X^2.Y^2 - X.Y = 6) is wrong. But can someone help me and explain how to factor this equation in the right way (I'm curious for know it).

Tks everybody
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Re: Simple equation on GMAT (help me) [#permalink]

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New post 09 Nov 2015, 04:28
phelipemariano wrote:
Guys, can you help me with this simple question about factoring an equation ?

A question on quantitative part in OG 2016 ask to solve Y in terms of X. The equation is X^2.Y^2 - X.Y = 6

I already know how to find de answer. What I would like to know is why the first step that I did wasn't correct. This was my first step to find the solution:

X^2.Y^2 - X.Y = 6
X.Y(X.Y - 1) -6 = 0
X.Y - 6 =0
X.Y = 6
Y = 6/X

X.Y(X.Y - 1) -6 = 0
X.Y - 1 = 0
X.Y = 1
Y = 1/X

I know that the factorization in the equation ( X^2.Y^2 - X.Y = 6) is wrong. But can someone help me and explain how to factor this equation in the right way (I'm curious for know it).

Tks everybody


This question is discussed here: if-xy-0-and-x-2-y-2-xy-6-which-of-the-following-could-be-y-126166.html

Factoring Quadratics: http://www.purplemath.com/modules/factquad.htm

Solving Quadratic Equations: http://www.purplemath.com/modules/solvquad.htm

Hope it helps.
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Simple equation on GMAT (help me) [#permalink]

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New post 09 Nov 2015, 20:34
phelipemariano wrote:
Guys, can you help me with this simple question about factoring an equation ?

A question on quantitative part in OG 2016 ask to solve Y in terms of X. The equation is X^2.Y^2 - X.Y = 6

I already know how to find de answer. What I would like to know is why the first step that I did wasn't correct. This was my first step to find the solution:

X^2.Y^2 - X.Y = 6
X.Y(X.Y - 1) -6 = 0
X.Y - 6 =0
X.Y = 6
Y = 6/X

X.Y(X.Y - 1) -6 = 0
X.Y - 1 = 0
X.Y = 1
Y = 1/X

I know that the factorization in the equation ( X^2.Y^2 - X.Y = 6) is wrong. But can someone help me and explain how to factor this equation in the right way (I'm curious for know it).

Tks everybody


To point out the error you have made here, I ask you to think about this:
How will you solve: \(a(a - 1) - 6 = 0\) ?
Is it the same as: \((a - 1)(a - 6) = 0\) ?

Note that the two are not same.
\(a(a - 1) - 6 = 0\) actually is \(a^2 - a - 6 = 0\)
\((a - 1)(a - 6) = 0\) actually is \(a^2 - 7a + 6 = 0\)

What is the same as \((a - 1)(a - 6) = 0\) ?
When you have \(a(a - 1) - 6(a - 1) = 0\), then you can take (a - 1) common and you are left with \((a - 1)(a - 6) = 0\)

Hope this helps.
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Simple equation on GMAT (help me)   [#permalink] 09 Nov 2015, 20:34
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