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# If xy ≠ 0, is 1/x +1/y = 16?

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Intern
Joined: 23 Nov 2014
Posts: 1
If xy ≠ 0, is 1/x +1/y = 16? [#permalink]

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23 Nov 2014, 05:41
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15% (low)

Question Stats:

78% (00:43) correct 22% (01:20) wrong based on 107 sessions

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If xy ≠ 0, is 1/x +1/y = 16?

(1) x + y = 16xy

(2) x = y
Math Expert
Joined: 02 Sep 2009
Posts: 47080
Re: If xy ≠ 0, is 1/x +1/y = 16? [#permalink]

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23 Nov 2014, 05:54
If xy ≠ 0, is 1/x +1/y = 16?

(1) x + y = 16xy --> divide by xy: x/(xy) + y/(xy) = 16 --> 1/y + 1/x = 16. Sufficient.

(2) x = y --> the question becomes whether 1/x + 1/x = 16 or whether x = 1/8. We cannot answer this, thus the statement is not sufficient.

Hope it's clear.
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Joined: 21 Jan 2014
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WE: General Management (Non-Profit and Government)
Re: If xy ≠ 0, is 1/x +1/y = 16? [#permalink]

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24 Nov 2014, 00:47
Given xy ≠ 0,
Solving this equation further 1/x +1/y = 16
(x+y)/xy=16...............A

1) x+y=16xy;
Inserting the value for x+y in equation A equates the both sides.SUFFICIENT.

2)x=y;
This will give any definite result for the equation A.
L.H.S ≠R.H.S INSUFFICIENT

Director
Joined: 04 Dec 2015
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Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
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Re: If xy ≠ 0, is 1/x +1/y = 16? [#permalink]

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09 Aug 2017, 22:08
blingbling wrote:
If xy ≠ 0, is 1/x +1/y = 16?

(1) x + y = 16xy

(2) x = y

(1) $$x + y = 16xy$$

$$\frac{x+ y}{xy} = 16$$

$$\frac{x}{xy} + \frac{y}{xy} = 16$$

$$\frac{1}{x} + \frac{1}{y} = 16$$

Hence I is Sufficient.

(2) $$x = y$$

We do not have value of either $$x$$ or $$y$$, hence we cannot find if $$\frac{1}{x} + \frac{1}{y} = 16$$

Hence II is Not Sufficient.

Re: If xy ≠ 0, is 1/x +1/y = 16?   [#permalink] 09 Aug 2017, 22:08
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