GMAT Prep - DS Number Properties

I feel ans should be 'E' here.

From 1: z <0
so, from the given equation (x+y)/z=-2

(x+y) should be >0 but we have no idea about y here.In sufficient

From 2: y>0

but no idea about z and x here.So in sufficient .

Combining both we know (x+y) >0 and y >0 , however we still can't find if x is < or > 0 . So insufficient.

When a question asks you for information about a specific variable, a great first step is to isolate that variable. So:

(x + y)/z = -2

x + y = -2z

x = -2z - y

And we want to know if x is positive.

(1) z < 0

no info about y, insufficient

(2) y > 0

no info about z, insufficient

Combined:

Since z is negative, -2z will be positive. Since y is positive, -y will be negative.

So, we know that x = (+) + (-) which could be + or - depending on the actual values we choose: insufficient, choose (e).

Thanks Stuart, that's a really good explanation and a very important tip to deal with such questions.