SAT stlye math problem?

Question

Let x Ω y be defined by x Ω y= (x-y)^2 for all values of x and y. If x Ω y= 2y Ω 3 and x= y-3, then which of the following could be the value of y?

 

A) -1

B) 1

C) 3

D) 4

E) 6

Answer 1

Since  x Ω y = 2y Ω 3, we have (x - y)² = (2y - 3)².  But, x = y - 3.

 

So, (y - 3 - y)² = (2y - 3)²

 

9 = 4y² - 12y + 9

 

4y² - 12y = 0

 

4y(y - 3) = 0

 

y = 0 or y = 3

 

ANSWER:  C