Is x a negative number?

Question

(1) x^2 is a positive number.

(2) x*|y| is not a positive number.

AKProdigy87 · Accepted Answer

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.

truplayer257 · Answer

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.

Posted from my mobile device

Zarrolou · Answer

Is x negative?

(i) x^2 is a positive number 
 x^2>0 , so  x
eq{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

summer101 · Answer

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.

Zarrolou · Answer

Mod of 0 is legit.

|0|=0

Bunuel · Answer

\

|0|=0.

Is x negative?

(1) x^2 is a positive number. This statement implies that  x
eq{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.

WholeLottaLove · Answer

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)

EMPOWERgmatRichC · Answer

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:  E

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

davidian22 · Answer

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.

Mayank1996 · Answer

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 .

Please give kudos if you found my posts helpful!

GMATwithAK · Answer

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

EMPOWERgmatRichC · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is x a negative number?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Is x a negative number?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards