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# (x^(-1) - y^(-1))/((xy)^(-1)(x - y)) =

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Manager
Joined: 29 Oct 2019
Posts: 235
(x^(-1) - y^(-1))/((xy)^(-1)(x - y)) =  [#permalink]

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Updated on: 11 Feb 2020, 01:34
5
00:00

Difficulty:

35% (medium)

Question Stats:

63% (01:14) correct 37% (02:05) wrong based on 67 sessions

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

(A) - 1

(B) 1

(C) - xy

(D) xy

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

Source: GMAT Quantum

Originally posted by sjuniv32 on 11 Feb 2020, 01:31.
Last edited by Bunuel on 11 Feb 2020, 01:34, edited 1 time in total.
Renamed the topic.
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4604
GMAT 1: 770 Q49 V46
Re: (x^(-1) - y^(-1))/((xy)^(-1)(x - y)) =  [#permalink]

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11 Feb 2020, 06:21
1
Top Contributor
sjuniv32 wrote:
$$\frac{x^{-1} - y^{-1} }{ (xy)^{-1} (x-y)}$$ =

(A) - 1

(B) 1

(C) - xy

(D) xy

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

Source: GMAT Quantum

Rather than deal with performing a variety of operations involving many fractions, a fast approach is to plug some values into the original expression.

Let's see what happens when x = 2 and y = 4

We get: $$\frac{x^{-1} - y^{-1} }{ (xy)^{-1} (x-y)}=\frac{2^{-1} - 4^{-1} }{ (2\times4)^{-1} (2-4)}$$

Aside: $$2^{-1}=\frac{1}{2}=0.5$$, $$4^{-1}=\frac{1}{4}=0.25$$ and $$8^{-1}=\frac{1}{8}=0.125$$

So we get: $$=\frac{0.5 - 0.25 }{ (8)^{-1} (-2)}$$

$$=\frac{0.5 - 0.25 }{ (0.125)(-2)}$$

$$=\frac{0.25 }{ -0.25}=-1$$

Since answer choice A is the only answer choice that evaluates to be -1 when x = 2 and y = 4, the correct answer is A

Cheers,
Brent
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Re: (x^(-1) - y^(-1))/((xy)^(-1)(x - y)) =  [#permalink]

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05 Mar 2020, 21:46
I have found the ps difficult to resolve. what are the related concepts to solve this?
Manager
Joined: 31 Jan 2020
Posts: 175
Re: (x^(-1) - y^(-1))/((xy)^(-1)(x - y)) =  [#permalink]

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06 Mar 2020, 02:04
1
moha20 wrote:
I have found the ps difficult to resolve. what are the related concepts to solve this?

I think it's probably simply to do with knowing how to "play around" with negative powers so that you can solve the equation. A suggestion to consider would be to take a simpler, smaller equation and play around with it. See what works and what doesn't.
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Joined: 29 Oct 2019
Posts: 235
Re: (x^(-1) - y^(-1))/((xy)^(-1)(x - y)) =  [#permalink]

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06 Mar 2020, 19:40
moha20 wrote:
I have found the ps difficult to resolve. what are the related concepts to solve this?

Hi

If you go through exponent chapter from the manhattan prep strategy guide, You can have all the basic concepts to resolve this.

Thank you.
Re: (x^(-1) - y^(-1))/((xy)^(-1)(x - y)) =   [#permalink] 06 Mar 2020, 19:40
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