The answer is E.

Statement 1: x^2 is a positive number.

x can either be positive or negative. Insufficient.

Statement 2: x*|y| is not a positive number.

There are two possible cases:

1st case: x*|y| < 0, therefore x must be negative.
2nd case: x*|y| = 0, therefore x or y can be zero, and this doesn't prove anything about x.

Therefore, insufficient.

Evaluating both Statements

We know that |x| > 0, and that x*|y| <= 0. If y is non-zero, X must be negative. However, if Y = 0, then it doesn't matter what X is. Insufficient.

Hi All,

This question can be solved by TESTing VALUES.

We're asked if X is a negative number. This is a YES/NO question.

Fact 1: X^2 is a positive number.

IF....
X = 2
X^2 = 4
The answer to the question is NO.

X = -2
X^2 = 4
The answer to the question is YES.
Fact 1 is INSUFFICIENT.

Fact 2: (X)|Y| is NOT a positive number.

IF....
Y = 0
X = 2
The answer to the question is NO.

Y = 0
X = -2
The answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, the two TESTs that we did in Fact 2 ALSO "fit" Fact 1, so we end up with NO and YES answers.
Combined, INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

The correct answer should be E. Note that we must not forget the case that x can equal 0 for statement 2, which means that x can be either 0 or negative.

Combining both statements, we know that x^2 is positive, but if y is 0, then x can be either positive or negative.

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1) x can be either positive or negative --> insufficient

2) if y = 0 --> then for any x, the product of x*|y| will not be positive. --> insufficient

Combined) no new information --> insufficient.

Hence, the answer is E.

Is x a negative number?

(1) x^2 is a positive number.

(2) x⋅|y| is not a positive number.

Solution:-

There is no information in the question stem to process so we move to the statements directly.

(1) x^2 is a positive number.

Square of any number is positive, be it a negative or a positive number.
So, X can be a negative number or a positive number as well. Hence, INSUFFICIENT

(2) x⋅|y| is not a positive number.

Now, We need to read this statement very carefully. It says x⋅|y| is NOT A POSITIVE number. It does not say that x⋅|y| is A NEGATIVE number. So, There are 2 possibilities now, x⋅|y| can either be a Negative number or it can be ZERO. (Because Zero is neither positive nor negative)
Lets say x⋅|y|=0
So, if |y|=0, X can either be positive or negative.
Lets say x⋅|y|= Negative
So, here X can only be negative.

Since, This statement is also not providing us a clear answer, Its INSUFFICIENT

Taking both statements together will do us no good because both statements suggest the same thing that X can either be positive or negative.

So the answer is E.


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From statement 1: x can be either positive or negative: Hence, insufficient.
From statement 2: x can be 0 or negative (If |y| is not 0). But x can also be positive if |y| = 0. So, basically x can be positive or negative or 0.

Even combining both the statements, doesn't help us narrow down on the scope of answers. Hence, E

I have a vert silly doubt

upon combining we get from 1-> x is either positive or negative
2-> x is either negative OR
Y is ZERO OR
X is zero

So when in 1 and 2 we are getting one scenario as x is negative, why is it not C?

Hi kri93

As I mentioned in the original quote, from 2: We also get that X can be positive, in the case when y = 0.
Therefore, even on combining 1 & 2, we have X can be positive or negative. Hence, E.

Hope this helps
Cheers

Answer (E)

x^2 will be positive or zero (if x=0)

x*|y| may be positive, negative or zero depending on whether x is postive/negative/zero or y is zero

Therefore, no conclusions can be drawn

Regards

Arun Krishnan
GMAT with AK
_________________

Hi Arun,

In Fact 1, we're told that X^2 is a POSITIVE number, so X itself could be positive OR negative (but NOT 0).

GMAT assassins aren't born, they're made,
Rich
_________________