Explanatory Answer
Alternatively, here is the text based explanation for the question.
The product of two numbers picked will be less than zero if one of the numbers is positive and the other is negative.
Statement 1 clearly indicates that neither x nor y is 0.
However, that alone is not sufficient because the probability of the product being less than 0 is dependent on how many of the 6 numbers is negative.
So, statement 1 is NOT sufficient.
Statement 2 points to the fact that the magnitude of x an y are same.
Both could be positive, both negative, one negative and the other positive or both zeroes.
However, the possibility of both being simultaneously positive or negative or zero can be eliminated as the question stem states that these are distinct integers. So, one of x or y has to be positive and the other negative.
So, we know that there are 4 positive numbers and 2 negative numbers.
Hence, we can determine the probability.
So, statement 2 is alone is sufficient.
Combining the two statements, we have no additional information other than what we have from statement 1.