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

Question

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

Bunuel · Accepted Answer

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.

unceldolan · Answer

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)

Bunuel · Answer

@ 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.

Similar questions to practice:
the-operation-is-defined-by-x-y-1-x-1-y-for-all-67650.html
gmat-prep-question-101282.html
if-the-operation-is-defined-by-x-y-xy-1-2-for-all-144272.html
an-operation-is-defined-by-the-equation-a-b-a-b-a-144074.html
let-denote-a-mathematical-operation-is-it-true-that-x-y-131347.html
for-any-operation-that-acts-on-two-numbers-x-and-y-the-127024.html
the-operation-is-defined-for-all-nonzero-numbers-a-and-b-106495.html
the-operation-x-n-for-all-positive-integers-greater-than-99064.html
for-all-integers-x-and-y-the-operation-is-defined-by-x-y-86208.html
the-operation-is-defined-for-all-nonzero-x-and-y-by-x-y-162019.html
the-operation-is-defined-for-all-integers-a-and-b-by-the-162119.html

Hope this helps.

unceldolan · Answer

Thank you! I guess I have to work myself into the topic. If I have any further questions, I won't hesitate to contact you

raharu · Answer

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 = ?
 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

KarishmaB · Answer

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

Bunuel · Answer

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.

apple08 · Answer

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

ENGRTOMBA2018 · Answer

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.

EMPOWERgmatRichC · Answer

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:  E

GMAT assassins aren't born, they're made,
Rich

apple08 · Answer

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

apple08 · Answer

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

mcelroytutoring · Answer

Attached is a visual that should help.

ScottTargetTestPrep · Answer

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

The answer is E.

ArnauG · Answer

To find the value of c given the equation a@c = 0, where the operation  is  defined as (a - b) / (a + b), we can substitute the given equation into the definition of @:

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

To solve for c, we can multiply both sides of the equation by (a + c) to eliminate the denominator:

(a - c) = 0

Now, we can isolate c by moving -c to the other side of the equation:

c = a

Therefore, the value of c is equal to a. Hence, the correct option is (E) a.

bumpbot · Answer

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.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards