if x plus y over z is equal to -2

[urooj.khan]

if x plus y over z is equal to -2, is x positive?

(1) z is negative
(2) y is positive

correct answer is e. i dont see how.

[stock.mojo11]

if x plus y over z is equal to -2, is x positive?

(1) z is negative
(2) y is positive

correct answer is e. i dont see how.

(x+y)/z=-2 means x+y =-2z

(1) z -ve

x+y =+ve X can be -ve/+ve/0 Insuff

(2) x+y =-2z

y +ve. X can be +ve/-ve/0

combined also x can +ve/-ve

Insuff

Just plug in numbers.

[RonPurewal]

the rephrase given in the above post is accurate, but it's a bit try-hard.

TAKEAWAY:
if a problem asks about a certain quantity or variable(s), then you should ISOLATE that quantity or variable(s).

this problem asks a question about x. therefore, you should isolate x.
if you do this, you get x = -y - 2z.

therefore, you have the rephrase you want:
is (-y - 2z) positive?

(1)
insufficient, because we don't know anything about -y (which could be any number at all, and which could definitely be big enough to overwhelm -2z).

(2)
insufficient, because we don't know anything about -2z (which could be any number at all, and which could definitely be big enough to overwhelm -y).

(together)
-y must be negative, but could be ANY negative number.
-2z must be positive, but could be ANY positive number.
the desired sum is therefore (arbitrary pos #) + (arbitrary neg #), which could work out to any number at all.
insufficient.

ans (e)