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

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Director
Joined: 12 Jun 2006
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Is x(x-y) positive? x<0 x<y [#permalink]  14 Dec 2006, 22:07
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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
Manager
Joined: 25 Sep 2006
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yes C

Why don't you post your reasoning and we see whats wrong.
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livin in a prison island...

Director
Joined: 12 Jun 2006
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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?
VP
Joined: 28 Mar 2006
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Re: DS: Number theory [#permalink]  15 Dec 2006, 04:08
ggarr wrote:
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

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
Senior Manager
Joined: 08 Jun 2006
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Location: Washington DC
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Going for C too..
It is good even when y = 0 or + ve
Director
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Quote:
-1^2 - 1(1) -1^2-(-1*1)=1+1=2=+ve

Thank you Sumithra .... carelessness
Senior Manager
Joined: 23 Jun 2006
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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.
Director
Joined: 12 Jun 2006
Posts: 536
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Kudos [?]: 29 [0], given: 1

Quote:
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
hobbit, how would you have reasoned this w/o picking at least one set of #s (i.e. [-1^2 - ((-1)(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.
Intern
Joined: 01 Dec 2006
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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.
Director
Joined: 12 Jun 2006
Posts: 536
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Quote:
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)

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.
SVP
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hobbit wrote:
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.

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.

ggarr wrote:
Quote:
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
hobbit, how would you have reasoned this w/o picking at least one set of #s (i.e. [-1^2 - ((-1)(0)) & -1^2 - ((-1)(1))])

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<y)

Since 1 and 2 combined gives us the second senario, we can determine that x(x-y) is indeed positive. Therefore C.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Manager
Joined: 18 Nov 2006
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Is x(x-y) positive?
x<0
x<y
----------------------------

Lesson: Pick numbers only when you can't do it with variables or in your head..

consider1)

x is -ve , y can be -ve or zero or +ve
now, whats the stem ? y is zero or +ve -> 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 [b]you can see answer is C.[/b]

TF, cant conclude from 1) Insuffi.

Take 2) x<y

say x is +ve, -> 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

Lesson: Pick numbers only when you can't do it with variables or in your head..
Intern
Joined: 01 Dec 2006
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ggarr,

you are right. thanks for correcting that.
VP
Joined: 14 May 2006
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hobbit wrote:
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.

halliluya thanks!
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