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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] New post 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] New post 13 Dec 2012, 09:16
Expert's post
Walkabout 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.

Answer: E.
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Re: An operation @ is defined by the equation a@b = (a - b) / (a [#permalink] New post 24 Nov 2013, 11:04
Bunuel wrote:
Walkabout 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.

Answer: E.


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] New post 24 Nov 2013, 12:47
Expert's post
unceldolan wrote:
Bunuel wrote:
Walkabout 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.

Answer: E.


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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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: An operation @ is defined by the equation a@b = (a - b) / (a [#permalink] New post 24 Nov 2013, 23:40
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An operation θ is defined by the equation... [#permalink] New post 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

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
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Re: An operation θ is defined by the equation... [#permalink] New post 08 Apr 2014, 22:11
Expert's post
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


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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Expert Post
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Joined: 02 Sep 2009
Posts: 19038
Followers: 3360

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Re: An operation θ is defined by the equation... [#permalink] New post 09 Apr 2014, 01:11
Expert's post
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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: An operation θ is defined by the equation...   [#permalink] 09 Apr 2014, 01:11
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