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 = ?

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

_________________

Karishma

Veritas Prep | GMAT Instructor

My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting

Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews