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# If xy > 0, 1/x + 1/y = 5, and 1/xy = 6, then (x+y)/5 = ?

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Math Expert
Joined: 02 Sep 2009
Posts: 42529

Kudos [?]: 135178 [0], given: 12671

If xy > 0, 1/x + 1/y = 5, and 1/xy = 6, then (x+y)/5 = ? [#permalink]

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09 Nov 2015, 23:02
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15% (low)

Question Stats:

68% (00:59) correct 32% (01:29) wrong based on 79 sessions

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If xy > 0, 1/x + 1/y = 5, and 1/xy = 6, then (x+y)/5 = ?

A. 1/25
B. 1/6
C. 1/5
D. 5
E. 6
[Reveal] Spoiler: OA

_________________

Kudos [?]: 135178 [0], given: 12671

Intern
Joined: 29 Aug 2015
Posts: 12

Kudos [?]: 4 [0], given: 8

Re: If xy > 0, 1/x + 1/y = 5, and 1/xy = 6, then (x+y)/5 = ? [#permalink]

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10 Nov 2015, 08:58

(1/X+1/Y)=5 canbe solved as {(x+y)/xy}=6. Substituting for 1/xy=6, we get
x+y=5/6

==> (x+y)/5= 5/(6*5)=1/6.

Kudos [?]: 4 [0], given: 8

VP
Joined: 22 May 2016
Posts: 1104

Kudos [?]: 392 [0], given: 639

If xy > 0, 1/x + 1/y = 5, and 1/xy = 6, then (x+y)/5 = ? [#permalink]

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23 Oct 2017, 10:14
Bunuel wrote:
If xy > 0, 1/x + 1/y = 5, and 1/xy = 6, then (x+y)/5 = ?

A. 1/25
B. 1/6
C. 1/5
D. 5
E. 6

HarrishGowtham wrote:

(1/X+1/Y)=5 canbe solved as {(x+y)/xy}=6. Substituting for 1/xy=6, we get
x+y=5/6

==> (x+y)/5= 5/(6*5)=1/6.

I am stuck trying to understand this explanation. I got the right answer, but not this way.

$$\frac{1}{x}+ \frac{1}{y} = 5$$

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

Aren't the two RHS equivalent?

Quote:
(1/X+1/Y)=5 can be solved as {(x+y)/xy}=6.

Can anyone explain the steps from the first part of the above sentence to the last part? If the two RHS above quote are equivalent, where does "= 6" come from?

Kudos [?]: 392 [0], given: 639

If xy > 0, 1/x + 1/y = 5, and 1/xy = 6, then (x+y)/5 = ?   [#permalink] 23 Oct 2017, 10:14
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