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# An operation @ is defined by the equation a@b = (a - b) / (a

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An operation @ is defined by the equation a@b = (a - b) / (a [#permalink]

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13 Dec 2012, 09:14
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An operation @ is defined by the equation a@b = (a - b) / (a + b), for all numbers a and b such that a ≠ -b. If a ≠ -c and a@c = 0, then c =

(A) -a
(B) -1/a
(C) 0
(D) 1/a
(E) a
[Reveal] Spoiler: OA
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Re: An operation @ is defined by the equation a@b = (a - b) / (a [#permalink]

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13 Dec 2012, 09:16
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An operation @ is defined by the equation a@b = (a - b) / (a + b), for all numbers a and b such that a ≠ -b. If a ≠ -c and a@c = 0, then c =

(A) -a
(B) -1/a
(C) 0
(D) 1/a
(E) a

Given that $$a@b = \frac{a - b}{a + b}$$, thus $$a@c = \frac{a - c}{a + c}$$.

Also given that $$a@c = \frac{a - c}{a + c}=0$$ --> $$a-c=0$$ --> $$a=c$$.

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Re: An operation @ is defined by the equation a@b = (a - b) / (a [#permalink]

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24 Nov 2013, 11:04
Bunuel wrote:
An operation @ is defined by the equation a@b = (a - b) / (a + b), for all numbers a and b such that a ≠ -b. If a ≠ -c and a@c = 0, then c =

(A) -a
(B) -1/a
(C) 0
(D) 1/a
(E) a

Given that $$a@b = \frac{a - b}{a + b}$$, thus $$a@c = \frac{a - c}{a + c}$$.

Also given that $$a@c = \frac{a - c}{a + c}=0$$ --> $$a-c=0$$ --> $$a=c$$.

Hi Bunnuel,

I've never senn such a task before in my life. Could you please explain what the @ means or what the whole expression "operation @" means? or do you recommend any books/links for this ? (I already worked through MGMAT Foundations of Math but really NEVER seen this before)
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Re: An operation @ is defined by the equation a@b = (a - b) / (a [#permalink]

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24 Nov 2013, 12:47
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unceldolan wrote:
Bunuel wrote:
An operation @ is defined by the equation a@b = (a - b) / (a + b), for all numbers a and b such that a ≠ -b. If a ≠ -c and a@c = 0, then c =

(A) -a
(B) -1/a
(C) 0
(D) 1/a
(E) a

Given that $$a@b = \frac{a - b}{a + b}$$, thus $$a@c = \frac{a - c}{a + c}$$.

Also given that $$a@c = \frac{a - c}{a + c}=0$$ --> $$a-c=0$$ --> $$a=c$$.

Hi Bunnuel,

I've never senn such a task before in my life. Could you please explain what the @ means or what the whole expression "operation @" means? or do you recommend any books/links for this ? (I already worked through MGMAT Foundations of Math but really NEVER seen this before)

@ is a made up operation (function), defined by the equation a@b = (a - b)/(a + b). For example 2@3=(2-3)/(2+3)=-1/5.

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Hope this helps.
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Re: An operation @ is defined by the equation a@b = (a - b) / (a [#permalink]

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24 Nov 2013, 23:40
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An operation θ is defined by the equation... [#permalink]

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08 Apr 2014, 19:35
Hello and thank you for your help! I don't understand the answer provided by my book.

Question:
An operation θ is defined by the equation a θ b = a-b/a+b, for all numbers a and b such that a does not equal -b. If a does not equal -c and a θ c = 0, then c = ?
[Reveal] Spoiler:
The correct answer is that c = a

Substitute c for b and 0 for a θ c in the given equation and solve for c.

So 0 = a - c / a + c

Multiply each side by a + c

So 0 = a - c
So c = a

My question is: why can they substitute c for b?

Source: 12th edition Gmat Review
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Re: An operation θ is defined by the equation... [#permalink]

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08 Apr 2014, 22:11
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raharu wrote:
Hello and thank you for your help! I don't understand the answer provided by my book.

Question:
An operation θ is defined by the equation a θ b = a-b/a+b, for all numbers a and b such that a does not equal -b. If a does not equal -c and a θ c = 0, then c = ?
[Reveal] Spoiler:
The correct answer is that c = a

Substitute c for b and 0 for a θ c in the given equation and solve for c.

So 0 = a - c / a + c

Multiply each side by a + c

So 0 = a - c
So c = a

My question is: why can they substitute c for b?

Source: 12th edition Gmat Review

θ has been defined as an operator which takes input values of two variables and gives the answer by calculating (First variable - Second variable)/(First variable + Second variable). Here a and b are just taken as an example.

a θ b = (a - b)/(a + b)
x θ y = (x - y)/(x + y)
a θ c = (a - c)/(a + c)
It doesn't what the two variables are.

Given a θ c = 0 = (a - c)/(a + c)
Then a - c = 0
a = c
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Math Expert Joined: 02 Sep 2009 Posts: 35837 Followers: 6827 Kudos [?]: 89636 [0], given: 10380 Re: An operation θ is defined by the equation... [#permalink] ### Show Tags 09 Apr 2014, 01:11 raharu wrote: Hello and thank you for your help! I don't understand the answer provided by my book. Question: An operation θ is defined by the equation a θ b = a-b/a+b, for all numbers a and b such that a does not equal -b. If a does not equal -c and a θ c = 0, then c = ? [Reveal] Spoiler: The correct answer is that c = a Answer: Substitute c for b and 0 for a θ c in the given equation and solve for c. So 0 = a - c / a + c Multiply each side by a + c So 0 = a - c So c = a My question is: why can they substitute c for b? Source: 12th edition Gmat Review Merging similar topics. Please refer to the discussion above. All OG13 questions are here: the-official-guide-quantitative-question-directory-143450.html P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 12834 Followers: 559 Kudos [?]: 157 [0], given: 0 Re: An operation @ is defined by the equation a@b = (a - b) / (a [#permalink] ### Show Tags 11 May 2015, 03:07 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Intern Joined: 17 May 2015 Posts: 27 Followers: 0 Kudos [?]: 4 [0], given: 40 Re: An operation is defined by the equation ab = (a - b) / (a [#permalink] ### Show Tags 27 Jul 2015, 06:49 Need great help How can I know that b can be substituted with c in the new equation ? Hope to hear from you Many thanks Math Forum Moderator Joined: 20 Mar 2014 Posts: 2647 GMAT 1: 750 Q49 V44 GPA: 3.7 WE: Engineering (Aerospace and Defense) Followers: 113 Kudos [?]: 1307 [0], given: 786 Re: An operation is defined by the equation ab = (a - b) / (a [#permalink] ### Show Tags 27 Jul 2015, 06:57 apple08 wrote: Need great help How can I know that b can be substituted with c in the new equation ? Hope to hear from you Many thanks The trick here is to recognize 2 things: 1. Unless you can substitute some variable by c in a@b , how are you going to get the desired relation between a and c? 2. The question stem mentions that the relation for a@b is true for "all numbers a and b". Thus you can substitute c for b and get the desired result. _________________ Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515 Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628 GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891 Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 7958 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 358 Kudos [?]: 2364 [1] , given: 163 An operation is defined by the equation ab = (a - b) / (a [#permalink] ### Show Tags 27 Jul 2015, 17:11 1 This post received KUDOS Expert's post Hi All, This question is an example of a 'Symbolism' question; in these types of prompt, the GMAT 'makes up' a math symbol, tells you how to use it, then asks you to use it to perform a calculation. Here, we're given a made-up calculation that uses the @ symbol.... A@B = (A-B)/(A+B) eg. 1@2 = (1-2)/(1+2) = -1/3 We're told that A@C = 0 and A ≠ -C. We're asked for the value of C.... We can TEST VALUES to answer this question, but we have to start by TESTing a VALUE for A, then figure out what C would have to equal.... IF.... A = 2 A@C = 2@C = (2-C)/(2+C) = 0 So, what would C have to equal to make this equation equal 0? (2-C)/(2+C) = 0 Since we're dealing with a fraction, we need the NUMERATOR to equal 0. In this example, that would ONLY happen when C = 2. So we're looking for an answer that equals 2 when A=2. Answer A: - A = -2 NOT a match Answer B: -1/A = -1/2 NOT a match Answer C: 0 NOT a match Answer D: 1/A = 1/2 NOT a match Answer E: A = 2 This IS a MATCH Final Answer: [Reveal] Spoiler: E GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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An operation is defined by the equation ab = (a - b) / (a [#permalink]

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27 Jul 2015, 21:27
Dear All, Many thanks ,
I'm sorry,i need help to understand it

Can I also know b can be replaced by c based on the following statements:
a not equal -b
a not equal -c
As it indicate a-b and a-c has same relationship , since it is the same relationship,I can substitute b with c. Appreciate your comments
Hope to hear from you many thanks for the great help

Last edited by apple08 on 28 Jul 2015, 06:08, edited 1 time in total.
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An operation is defined by the equation ab = (a - b) / (a [#permalink]

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27 Jul 2015, 21:53
Or since a@c = 0, I can plug c into b since @ is common in both a@b and a@c. How can I make use of "a not equal to -b" or "a not equal to -c"? Is it from "a not equal to -c" I know c is not equal to -a, hence eliminate answer (a) -a , really appreciate your great help, many many thanks
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Re: An operation is defined by the equation ab = (a - b) / (a [#permalink]

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25 May 2016, 21:23
Attached is a visual that should help.
Attachments

Screen Shot 2016-05-25 at 9.42.05 PM.png [ 76.69 KiB | Viewed 2094 times ]

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Re: An operation is defined by the equation ab = (a - b) / (a [#permalink]

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16 Jun 2016, 04:59
An operation @ is defined by the equation a@b = (a - b) / (a + b), for all numbers a and b such that a ≠ -b. If a ≠ -c and a@c = 0, then c =

(A) -a
(B) -1/a
(C) 0
(D) 1/a
(E) a

We are given that operation @ is defined by a@b = (a-b)/(a+b).

We are also given that a@c = 0; thus, according to the operation, all instances of a can remain and all instances of b will be replaced with variable c. We then set that entire expression to zero.

(a-c)/(a+c) = 0

We can multiply both sides of the equation by a+c and then solve for a:

a – c = 0

a = c

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Re: An operation is defined by the equation ab = (a - b) / (a   [#permalink] 16 Jun 2016, 04:59
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