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1/x + 1/y =6

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

Question Stats:

68% (01:39) correct 31% (01:43) wrong based on 35 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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Re: 1/x + 1/y =6 [#permalink] New post 16 Mar 2018, 16:20
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The question is wrong!
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Re: 1/x + 1/y =6 [#permalink] New post 17 Mar 2018, 23:45
No offence, but the question doesn't make much sense.
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GMAT Club Legend
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Re: 1/x + 1/y =6 [#permalink] New post 18 Mar 2018, 12:45
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FatemehAsgarinejad wrote:
The question is wrong!


Yeah.. Fixed my bad
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Re: 1/x + 1/y =6 [#permalink] New post 18 Mar 2018, 12:50
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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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Re: 1/x + 1/y =6 [#permalink] New post 21 Mar 2018, 12:02
answer: C
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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Re: 1/x + 1/y =6 [#permalink] New post 30 Mar 2018, 01:27
Answer is C

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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