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Simple equation on GMAT (help me)

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Joined: 09 Nov 2015
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Simple equation on GMAT (help me) [#permalink]

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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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Joined: 02 Sep 2009
Posts: 41699

Kudos [?]: 124810 [0], given: 12079

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

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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

Hope it helps.
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Kudos [?]: 124810 [0], given: 12079

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Location: Pune, India
Simple equation on GMAT (help me) [#permalink]

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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

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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