GMAT Prep - X & Y

[rosh26]

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,

[amitansu]

From 1: x-y=1/2 => x is positive

From 2: x/y>1 => both have to be +ve or -ve at the same time.

From 1 we know x is positive so, y has to be positive to satisfy 2nd statement as x/y to be positve or greater than 1.


Amit

[rosh26]

From 1, how do you get that x is positive?

can't a negative (X) minus a negative (Y) = positive?

[Ian Stewart]

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:

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.

[rosh26]

Excellent Solution! Thanks a lot Ian!!!!!!!!!!