GMAT Prep - X & Y

First, I'd note that Statement 1 does not mean that x is positive. x could be -7, and y could be -7.5, for example.

Now back to the original post:

rosh26 wrote:Ok Here's what I got so far:

Stmt I: can reduce to x-y=1/2

Stmt II: x/y> 1

So, from stmt II x/y are both positive or negative, and from stmt 1 x-y = 1/2

So I chose E and am wondering why answer is C.

Thanks,

The lone problem here is that you're not using all of the information given. The conclusion you've drawn from Statement 2 is that x and y have the same sign (both positive or both negative). That's certainly true, but you could have concluded that from the statement "x/y > 0." You're told even more than that; you know that "x/y > 1." From this:

x/y > 1

Either
a) x and y are both positive *and* x > y
or
b) and y are both negative *and* x < y

From Statement 1, we know that x > y, so case b) above is impossible. So x and y must both be positive if we use both statements. C.

Alternatively, you know:

x = y + 1/2

You also know x/y > 1. Use substitution:

(y + 1/2)/y > 1
y/y + (1/2)/y > 1
1 + 1/2y > 1
1/2y > 0
y > 0

And from here, x is positive as well.