My answer is B.
The question is asking if x <0. We should look for statements that give a definite YES/NO answer.
Stmt 1: The answer we get is Yes & No. Since, there is no definite answer, this statement is insufficient.
Stmt 2: x*|y| < 0. Since |y| will always yield a positive number, x has to be -ve. This statement is sufficient to answer our main question.
Is x Negative?
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Source: Beat The GMAT — Data Sufficiency |
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nitya34
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What about |y|=0? 
Vemuri wrote:My answer is B.
The question is asking if x <0. We should look for statements that give a definite YES/NO answer.
Stmt 1: The answer we get is Yes & No. Since, there is no definite answer, this statement is insufficient.
Stmt 2: x*|y| < 0. Since |y| will always yield a positive number, x has to be -ve. This statement is sufficient to answer our main question.
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Morgoth
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nitya34 wrote:Is x a negative number?
statement 1: x^2 is a positive number
statement 2: x*lyl is not a positive number
I believe its not E its C
x < 0 ?
Statement I
x^2 is a positive number
this means x is negative or positive but not 0.
insufficient.
Statement II
x*lyl is not a positive number
this means the above expression is either negative or 0
x could be negative or positive.
insufficient.
Combining I & II
x^2 is positive number
x*lyl is not a positive number
Case I
if x is negative & y is negative, x*lyl will always be negative since lyl will always be positive.
Case II
if x is positive & y = 0 x*lyl will be 0
Case III
if x is negative & y=0 x*lyl will be 0
Hence x could be negative or positive.
Insufficient.
Thus, E.
Hope this helps.
