Target question: Is \(\frac{y}{x} < 1\) ?
This is a good candidate for rephrasing the target question.

Since x is NEGATIVE, we can take: \(\frac{y}{x} < 1\)...
...and multiply both sides by x to get: \(y > x\) [aside: since we multiplied both sides of an inequality by a negative value, we reverse the direction of the inequality symbol]

REPHRASED target question: Is \(y > x\) ?
Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

Once we've rephrased the target question, we can easily deal with the two statements

Statement 1: \(y < x\)
So, the answer to the REPHRASED target question is NO, y is NOT greater than x
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: \(y < 0\)
So we now know that x and y are both negative.
This is not enough information to answer the REPHRASED target question. Here are two possible cases:
Case a: x = -1 and y = -2. In this case, the answer to the REPHRASED target question is NO, y is NOT greater than x
Case b: x = -2 and y = -1. In this case, the answer to the REPHRASED target question is YES, y IS greater than x
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
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given
x<0
x is -ve
and find y/x<1
#1
y<x
so if x = -1 , y =-2
so y/x<1 ; no
sufficient
#2
y<0
in that case y=x is possible so we get both yes and no for y/x<1
Insufficient
IMO A

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