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An operation @ is defined by the equation a@b = (a  b) / (a
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13 Dec 2012, 10:14
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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
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Re: An operation @ is defined by the equation a@b = (a  b) / (a
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13 Dec 2012, 10:16




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Re: An operation @ is defined by the equation a@b = (a  b) / (a
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24 Nov 2013, 12:04
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 \(a@c = \frac{a  c}{a + c}=0\) > \(ac=0\) > \(a=c\). 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
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24 Nov 2013, 13:47



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Re: An operation @ is defined by the equation a@b = (a  b) / (a
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25 Nov 2013, 00:40
Bunuel wrote: 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



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An operation θ is defined by the equation...
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08 Apr 2014, 20:35
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 = ab/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



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Re: An operation θ is defined by the equation...
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08 Apr 2014, 23:11
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 = ab/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 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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Re: An operation θ is defined by the equation...
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09 Apr 2014, 02:11



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Re: An operation is defined by the equation ab = (a  b) / (a
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27 Jul 2015, 07:49
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



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Re: An operation is defined by the equation ab = (a  b) / (a
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27 Jul 2015, 07:57
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.



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An operation is defined by the equation ab = (a  b) / (a
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27 Jul 2015, 18:11
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 madeup calculation that uses the @ symbol.... A@B = (AB)/(A+B) eg. 1@2 = (12)/(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 = (2C)/(2+C) = 0 So, what would C have to equal to make this equation equal 0? (2C)/(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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An operation is defined by the equation ab = (a  b) / (a
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Updated on: 28 Jul 2015, 07:08
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 ab and ac 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
Originally posted by apple08 on 27 Jul 2015, 22:27.
Last edited by apple08 on 28 Jul 2015, 07:08, edited 1 time in total.



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An operation is defined by the equation ab = (a  b) / (a
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27 Jul 2015, 22:53
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
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25 May 2016, 22:23
Attached is a visual that should help.
Attachments
Screen Shot 20160525 at 9.42.05 PM.png [ 76.69 KiB  Viewed 9646 times ]
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Re: An operation is defined by the equation ab = (a  b) / (a
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16 Jun 2016, 05:59
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 We are given that operation @ is defined by a@b = (ab)/(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. (ac)/(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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