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# For positive integers x and y, xy is defined by xy=(x+y)/xy. If a, b

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6823
GMAT 1: 760 Q51 V42
GPA: 3.82
For positive integers x and y, xy is defined by xy=(x+y)/xy. If a, b  [#permalink]

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Updated on: 28 Nov 2017, 00:02
00:00

Difficulty:

65% (hard)

Question Stats:

56% (02:16) correct 44% (03:09) wrong based on 102 sessions

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[GMAT math practice question]

For positive integers $$x$$ and $$y$$, $$x@y$$ is defined by $$x@y=\frac{(x+y)}{xy}$$. If $$a, b$$, and $$c$$ are positive integers, what is the value of $$\frac{1}{a}$$@1/$$(\frac{1}{b}@\frac{1}{c})$$?

A. $$a+b+c$$
B. $$\frac{1}{abc}$$
C. $$\frac{1}{(a+b+c)}$$
D. $$\frac{1}{(ab+bc+ca)}$$
E. $$\frac{3}{abc}$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 27 Nov 2017, 23:58. Last edited by MathRevolution on 28 Nov 2017, 00:02, edited 1 time in total. Manager Joined: 27 Dec 2016 Posts: 236 Concentration: Marketing, Social Entrepreneurship GPA: 3.65 WE: Marketing (Education) Re: For positive integers x and y, xy is defined by xy=(x+y)/xy. If a, b [#permalink] ### Show Tags 28 Nov 2017, 00:00 1 MathRevolution wrote: [GMAT math practice question] For positive integers $$x$$ and $$y$$, $$x@y$$ is defined by $$x@y=\frac{(x+y)}{xy}$$. If $$a, b$$, and $$c$$ are positive integers, what is the value of $$\frac{1}{a}@\frac{1}{([fraction]1/b}@\frac{1}{c})[/fraction]$$? A. $$a+b+c$$ B. $$\frac{1}{abc}$$ C. $$\frac{1}{(a+b+c)}$$ D. $$\frac{1}{(ab+bc+ca)}$$ E. $$\frac{3}{abc}$$ MathRevolution, please edit your question to make it clearer to read... _________________ There's an app for that - Steve Jobs. Math Expert Joined: 02 Sep 2009 Posts: 52343 Re: For positive integers x and y, xy is defined by xy=(x+y)/xy. If a, b [#permalink] ### Show Tags 28 Nov 2017, 00:05 MathRevolution wrote: [GMAT math practice question] For positive integers $$x$$ and $$y$$, $$x@y$$ is defined by $$x@y=\frac{(x+y)}{xy}$$. If $$a, b$$, and $$c$$ are positive integers, what is the value of $$\frac{1}{a}$$@1/$$(\frac{1}{b}@\frac{1}{c})$$? A. $$a+b+c$$ B. $$\frac{1}{abc}$$ C. $$\frac{1}{(a+b+c)}$$ D. $$\frac{1}{(ab+bc+ca)}$$ E. $$\frac{3}{abc}$$ Similar question: https://gmatclub.com/forum/when-x-y-are ... 19963.html _________________ Intern Joined: 28 Apr 2017 Posts: 39 Re: For positive integers x and y, xy is defined by xy=(x+y)/xy. If a, b [#permalink] ### Show Tags 28 Nov 2017, 10:59 Formatting issue led to confusion Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6823 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: For positive integers x and y, xy is defined by xy=(x+y)/xy. If a, b [#permalink] ### Show Tags 30 Nov 2017, 00:28 => => We can simplify the definition of the operation in the following way: x@y=(x+y)/xy = x/(xy) + y/(xy) = 1/x+1/y. So, 1/a@1/(1/b@1/c) = a + (1/b @1/ c) = a + ( b + c ). Therefore, the answer is A. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Joined: 13 Nov 2017
Posts: 1
Re: For positive integers x and y, xy is defined by xy=(x+y)/xy. If a, b  [#permalink]

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06 Dec 2017, 11:42
MathRevolution wrote:
=>
=>

x@y=(x+y)/xy = x/(xy) + y/(xy) = 1/x+1/y.
So,
1/a@1/(1/b@1/c) = a + (1/b @1/ c) = a + ( b + c ).

Hello,

I don't get why you are performing a sum instead of the division you asked in the question.

You are saying: 1/a@1/(1/b@1/c) = a + (1/b @1/ c) = a + ( b + c ).

But as I see, it would be= 1/a@1/(1/b@1/c) = 1+a / b+c

Please tell me what I am doing wrong.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6823
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: For positive integers x and y, xy is defined by xy=(x+y)/xy. If a, b  [#permalink]

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16 Dec 2017, 23:19
arrugev93 wrote:
MathRevolution wrote:
=>
=>

x@y=(x+y)/xy = x/(xy) + y/(xy) = 1/x+1/y.
So,
1/a@1/(1/b@1/c) = a + (1/b @1/ c) = a + ( b + c ).

Hello,

I don't get why you are performing a sum instead of the division you asked in the question.

You are saying: 1/a@1/(1/b@1/c) = a + (1/b @1/ c) = a + ( b + c ).

But as I see, it would be= 1/a@1/(1/b@1/c) = 1+a / b+c

Please tell me what I am doing wrong.

Sum of reciprocals is much easier than other methods.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 05 Oct 2017
Posts: 2
Re: For positive integers x and y, xy is defined by xy=(x+y)/xy. If a, b  [#permalink]

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19 Dec 2017, 10:12
I do not understand the solution.
I am getting 1+a/ (b+c)
Re: For positive integers x and y, xy is defined by xy=(x+y)/xy. If a, b &nbs [#permalink] 19 Dec 2017, 10:12
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