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# 1/x + 1/y =6

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Joined: 07 Jun 2014
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1/x + 1/y =6 [#permalink]  16 Mar 2018, 16:14
Expert's post
00:00

Question Stats:

71% (01:38) correct 28% (01:43) wrong based on 39 sessions
$$\frac{1}{x} + \frac{1}{y} =6$$

$$\frac{-1}{3} = -2\frac{zy}{z+y}$$

 Quantity A Quantity B z x

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Drill 1
Question: 9
Page: 498-499
[Reveal] Spoiler: OA

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Sandy
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Manager
Joined: 22 Feb 2018
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Re: 1/x + 1/y =6 [#permalink]  16 Mar 2018, 16:20
1
KUDOS
The question is wrong!
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Manager
Joined: 15 Feb 2018
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Kudos [?]: 17 [0], given: 33

Re: 1/x + 1/y =6 [#permalink]  17 Mar 2018, 23:45
No offence, but the question doesn't make much sense.
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 102

Kudos [?]: 1741 [1] , given: 397

Re: 1/x + 1/y =6 [#permalink]  18 Mar 2018, 12:45
1
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Expert's post
The question is wrong!

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4856
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 102

Kudos [?]: 1741 [1] , given: 397

Re: 1/x + 1/y =6 [#permalink]  18 Mar 2018, 12:50
1
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Expert's post
Explanation

Using the Bowtie method, you find that $$\frac{x+y}{xy}$$=6.

By multiplying both sides of the second equation by $$\frac{-1}{2}$$, you find that $$\frac{1}{6}=\frac{zy}{z+y}$$.

Flipping both fractions yields $$\frac{z+y}{zy}=6$$, and thus, $$\frac{z+y}{zy}=\frac{x+y}{xy}$$.

Inspecting the two fractions, you may realize that z must equal x.

Alternatively, by applying the Bowtie again, you obtain $$\frac{y + x}{zy} = \frac{z + y}{xy}$$, and thus $$zy^2 + xyz = xyz + xy^2$$, meaning $$zy^2 = xy^2$$, or z = x, so the answer is choice (C).
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Manager
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Re: 1/x + 1/y =6 [#permalink]  21 Mar 2018, 12:02
1/x + 1/y = 6
(x + y) / xy = 6

-1/3 = -2 (zy/(z + y))
(z + y) / zy = 6

(x + y) / xy = (z + y) / zy
(x + y) / x = (z + y) / z
1 + y/x = 1 + y/z
y/x = y/z
1/x = 1/z
x = z

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Intern
Joined: 28 Nov 2017
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Kudos [?]: 34 [0], given: 25

Re: 1/x + 1/y =6 [#permalink]  30 Mar 2018, 01:27

Expand the 1st given Equation and you get 6 = x+y / xy

Expand the 2nd Eqn and you will get 1/6 = zy/y+z

Substitute the value of 6 from 1st Equation and you get the answer after cancelling the common terms both sides.
Re: 1/x + 1/y =6   [#permalink] 30 Mar 2018, 01:27
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