If xy < zy < 0, is y positive?

[BTGModeratorVI]

If xy < zy < 0, is y positive?

(1) x < z
(2) x is negative

Answer: D
Source: Veritas

[Brent@GMATPrepNow]

If xy < zy < 0, is y positive?

(1) x < z
(2) x is negative

Answer: D
Source: Veritas

Target question: Is y positive?

Given: xy < zy < 0,
Let's focus on this part of the inequality: xy < zy
Subtract xy from both sides to get: 0 < zy - xy
Factor out the y to get: 0 < y(z - x) (this will come in handy later)

Statement 1: x < z
Subtract x from both sides to get: 0 < z - x
In other words, (z - x) is POSITIVE
This means we can take our given inequality 0 < y(z - x) and divide both sides by (z - x) to get: 0 < y
So, the answer to the target question is YES, y IS positive
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x is negative
The given information tells us that xy < zy < 0
This means xy < 0
In other words, xy is NEGATIVE
So, if x is negative, then it MUST be the case that y is POSITIVE
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent