cschmidlapp Wrote:This question came up in my last CAT.
"If y is not equal to 4, x is not equal to 0, and y^2-16/3x = y-4/6, then in terms of x, y equals?"
granted, it can be difficult to format mathematical expressions on a forum, but please try to format these statements so that they are easier to read and less ambiguous.
from context, it appears that this statement is supposed to say ...
(y^2 - 16) / 3x = (y - 4) / 6
is that what it's supposed to say? please confirm, thanks.
disclaimer: the explanations below assume that my formulation of the problem is correct.
I have two questions - if y is not equal to 4, what is the math rule that allows you to eliminate the two (y-4)s when they aren't set equal to 0?
if y is not 4, then (y - 4) is nonzero. so, you can divide both sides of the equation by (y - 4), in the same way that you could divide both sides by, say, 3 or 16 or 100.
Second - in the MGMAT explanation, once simplified, you get down to y+4 = x/2, but then the next step and answer is y = x-8/2. How do you get the 8? Shouldn't it be x/2-4?
again, the notation is somewhat ambiguous here, but i'll assume that the expressions are supposed to be (x - 8) / 2 and (x/2) - 4.
if those are the right expressions, then they are equivalent to each other.
in your expression (x/2) - 4, just make a common denominator:
x/2 - 8/2
then subtract the expressions, and you'll get the other expression.