xy < zy < 0
Both xy and zy are negative.
Either y is negative, x and z both are positive and x > z.
Or y is positive, x and z both are negative and x < z.

Question: Is y positive?

(1) x < z
If x < z, x and z are both negative and y is positive. Sufficient.

(2) x is negative
If x is negative, z is also negative and then y must be positive. Sufficient.

Answer (D)
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If xy < zy < 0, is y positive?

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


When you modify the original condition and the question, it becomes (x-z)y<0에서 y>0? --> x-z<0?. x<Z에서 1) is yes, which is sufficient.
For 2), if x<0, y>0 derived from xy<0, which is yes and sufficient. Therefore, the answer is D.


 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
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Dividing an inequality by a variable whose sign is UNKNOWN is the biggest mistake you can make in inequality questions.

The sign of the inequality changes if you divide or multiply by a negative number. This is the reason why you CAN NOT divide by y.

If xy<zy ---> y*(x-z)<0 --> this means that either

Case 1: y>0 and x-z<0 OR
Case 2: y<0 and x-z>0

When you divide by y WITHOUT reversing the signs, you are inherently assuming that y>0. This is the very question asked.