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If xy is different from zero [#permalink]
Expert's post 00:00

Question Stats: 81% (00:36) correct 18% (00:49) wrong based on 72 sessions
If $$xy \neq 0$$, $$\frac{x - 1}{xy} =$$

(A) $$\frac{1}{x} - \frac{1}{xy}$$

(B) $$\frac{x}{y} - \frac{1}{xy}$$

(C) $$\frac{1}{y} - x$$

(D) $$\frac{1}{y} - \frac{1}{xy}$$

(E) $$\frac{1}{xy} - \frac{1}{y}$$
[Reveal] Spoiler: OA

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Re: If xy is different from zero [#permalink]
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Expert's post
Firstly, the xy≠0 part here isn't important. It's merely to satisfy any math nerds out there who would protest that if xy = 0, this question is undefined. Nerds!

Secondly, let's solve this. When you have a fraction with terms being added or subtracted in the denominator, a good thought is to split it into two fractions. Thus:

x-1
xy

can be split into
x - 1
xy xy

which simplifies to
1 - 1
y xy

METHOD TWO: Another way to solve this problem, or almost any other problem with variables in the answer choices, would be to pick a couple of values for x and y, for example 2 and 3, respectively, and plug them into the original equation. This results in a value of 1/6. Then plug 2 and 3 into every answer you see, and you will find that only answer choice D results in a value of 1/6. Thus, only D can be the correct answer.
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GRE Instructor Joined: 10 Apr 2015
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Re: If xy is different from zero [#permalink]
Expert's post
Carcass wrote:
If $$xy \neq 0$$, $$\frac{x - 1}{xy} =$$

(A) $$\frac{1}{x} - \frac{1}{xy}$$

(B) $$\frac{x}{y} - \frac{1}{xy}$$

(C) $$\frac{1}{y} - x$$

(D) $$\frac{1}{y} - \frac{1}{xy}$$

(E) $$\frac{1}{xy} - \frac{1}{y}$$

----------ASIDE-------------------
The GRE loves to test your knowledge of the following identities:

$$\frac{a + b}{c} = \frac{a}{c} + \frac{b}{c}$$

$$\frac{a - b}{c} = \frac{a}{c} - \frac{b}{c}$$

---ONTO THE QUESTION!----------------------------------------

So we can write: $$\frac{x - 1}{xy} = \frac{x}{xy} - \frac{1}{xy}$$

Simplify first fraction to get: $$= \frac{1}{y} - \frac{1}{xy}$$

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course. Manager Joined: 27 Feb 2017
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Re: If xy is different from zero [#permalink]
the way I did this was basically workout each option and also workout the equation in the question Re: If xy is different from zero   [#permalink] 02 May 2018, 11:37
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