Is x a negative number?

Is x negative?

(i) x^2 is a positive number
\(x^2>0\), so \(x\neq{0}\), not sufficient to say that it is negative.

(ii) x * |y| is not a positive number
\(x*|y|\leq{0}\), so y could be 0 and x could have any value (positive, negative, or zero) and this would be respected
Not sufficient.

1+2)Still y could be 0, and in this case x, which now we know cannot be zero, could still equal a positive or negative number.
Example \(2*0\leq{0}\) this respects both conditions and x is positive, or \(-2*0\leq{0}\) here x is negative.
Not sufficient
E

Hi Zarrolou,
I thought mod of Zero was illegal.
in (ii) x could be zero. But together we know x cannot be zero hence negative.

Mod of 0 is legit.

\(|0|=0\)

\

|0|=0.

Is x negative?

(1) x^2 is a positive number. This statement implies that \(x\neq{0}\). Not sufficient.

(2) x * |y| is not a positive number --> \(x * |y|\leq{0}\). If \(y=0\), then \(x\) could be ANY number. Not sufficient.

(1)+(2) Again, if \(y=0\), then \(x\) could be ANY number but 0 (excluded because of the first statement). Not sufficient.

Answer: E.

Is x negative?


(1) x^2 is a positive number

x^2 = +
|x| = +
x could be any number aside from zero and |x| will be positive.
x = positive or negative
INSUFFICIENT

(2) x * |y| is not a positive number
|y| will always be a positive number so for x * |y| to be negative x must be negative.
HOWEVER, the answer could be zero too. 0 is not positive or negative. So, 0 * |y| = 0 OR x * |0| = 0.
x = positive, zero or negative
INSUFFICIENT

1+2) # 1 tells us that x could be positive or negative. # 2 tells us that c could be positive, negative or zero. In other words, x could be positive or negative.
INSUFFICIENT

(E)

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

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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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

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