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

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)

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

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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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

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:

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

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.
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