“For Positive Numbers (p - q)/(p + q)”: Is it correct to say that because the equation has 2 variables, I can't solve the problem?

Question

Is it correct to say that because the equation has 2 variables, I can't solve the problem? Can I reach a similar conclusion for answer D? Why do you compare only 1/(p+q) = 2/3? I think in the equation it remained p-q on the top, too.

Answer

While sometimes you might run into a situation where you can manage to solve for at least one of the variables in an equation, in general you're correct. If we try to solve for this equation we get the following:

(p-q) / (p+q) = 2/3

3 (p-q) = 2 (p+q)

3p - 3q = 2p + 2q

5p = 5q

p = q

This doesn't really help us very much! But really the principle that we are hoping to explain in the explanation is that if we have the following:

x/y = 2/3

We cannot say that:

x = 2 and y = 3

because we could have the following:

x = 6, y = 9

x/y = 2/3

6/9 = 2/3

2/3 = 2/3

This works as well. If you chose D based on trying to solve the equation, then that works perfectly fine as well.

Link

http://gre.magoosh.com/questions/2601