Is x(x-y) positive? x

Question

I don't understand why the answer is what it is. I'll post my thoughts later. Maybe someone can let me know where my reasoning is off.

Is x(x-y) positive?
x<0
x<y
 Please explain your answers

Viperace · Answer

yes C

Why don't you post your reasoning and we see whats wrong.

ggarr · Answer

I picked E. 
We all agree that neither (1) nor (2) is independently sufficient.

x(x-y) = x^2 - xy

  Picking #s  

(1) x<0 
(2) x<y 

Based on (1) and (2) it seems as though y can be 0 or 1.

 Scenario A: 
x^2 - xy
-1^2 - 1(0)
1

 Scenario B: 
-1^2 - 1(1)
0

Two different #s using (1) and (2). Insufficient. 
 Where did I go wrong?

trivikram · Answer

from I it is INSUFF

from II x-y<0 this is needed 'cos who knows if x=y??

so I and II are needed

anindyat · Answer

Going for C too..
It is good even when y = 0 or + ve

ggarr · Answer

Thank you Sumithra ....  carelessness

hobbit · Answer

there is a lesson in ggarr's mistake.

virtually all books/gmat courses teach the power of "picking number" strategies...

however, at least from what i understand, very rarely teach when NOT to you it. it can be an hazardous methodology sometimes....

the more obvious cases are when 1,2,3 and even 4 examples that "goes right" doesn't tell us that something will always (for any number)"go right".
this usually happens in DS questions, but not always...

the other, less obvious case when you SHOULD avoid "picking numbers", is where this method creates lots of "work", that is, computations and arihmetics. especially if these involve fractions, negative numbers and exponents.

most of us will eventually will do some mistakes in calculations.

true.... we can be careful and avoid those mistake (a wise move)... but, we can altogether avoid the computation itself.

like in this question. in order to find if a multiplication is positive or negative we should just ask if each component is positive or negative... not try numbers to see whats happenning there....

i claimed before and i still claim, succeeding gmat quant is not about knowing enough math techniques for solving problems, but rathr - using as few math skills as possible to solve them.

just my two pence.

ggarr · Answer

hobbit, how would you have reasoned this w/o picking  at least  one set of #s (i.e.  0 )) & -1^2 - ((-1)( 1 ))])

I know in order to be safe picking #s I should've tried fractions too. In that way, this methodology is flawed. Anyone, please explain how you approached/would approach this prob.

kpcronin · Answer

I'll give this a shot...

I mutliplied it out.

x^2 - xy

Now, x < 0 so x must be negative and the first half of the above equation is positive (x^2).

So you have POSITIVE NUMBER - (NEGATIVE NUMBER)Y

Statement 2 says that x < y, so y is either 0 or positive. 

Now you have POSITIVE NUMBER - (NEGATIVE NUMBER)0

OR 

POSITIVE NUMBER - (NEGATIVE NUMBER)(NEGATIVE NUMBER)

Hope that helps.

ggarr · Answer

kpcronin,

Did you mean  POSITIVE NUMBER - (NEGATIVE NUMBER)( POSITIVE NUMBER  ) instead of POSITIVE NUMBER - (NEGATIVE NUMBER)(NEGATIVE NUMBER)?
I like your explanation. I just wanna make sure I fully understand it.

HongHu · Answer

Great comment. I couldn't agree more. For each question there may be multiple ways to solve it. Some of them may need to use more advanced math concepts and skills. But most GMAT questions can be solved using the most basic math skills. As hobbit said, you shouldn't use picking numbers for this question. x(x-y) can be positive in two scenarios: a. x>0, x-y>0 (meaning x>y) b. x<0, x-y<0 (meaning x

BLISSFUL · Answer

Is x(x-y) positive? x<0 x stem is +ve. but y is -ve then if y is < x ..stem is -ve if y is >x , then stem is +ve ( here look at 2) and you can see answer is C. TF, cant conclude from 1) Insuffi. Take 2) x y is also +ve and >x _> stem is -ve say x is -ve -> y can be +ve or -ve or zero based on y value, stem can be -ve or +ve cant conclude .. insuffi.. Take both: stem is +ve therefore a nswer is C. Lesson: Pick numbers only when you can't do it with variables or in your head..

kpcronin · Answer

ggarr,

you are right. thanks for correcting that.

u2lover · Answer

halliluya :pray thanks!

Is x(x-y) positive? x<0 x<y

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