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# Is A positive? 1. x^2-2*x+A is positive for all x 2. A*x^2+1

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Senior Manager
Joined: 18 Jun 2007
Posts: 274
Is A positive? 1. x^2-2*x+A is positive for all x 2. A*x^2+1 [#permalink]

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17 Oct 2008, 11:04
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Is A positive?
1. x^2-2*x+A is positive for all x
2. A*x^2+1 is positive for all x

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
VP
Joined: 17 Jun 2008
Posts: 1479
Re: DS: A positive [#permalink]

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17 Oct 2008, 12:05
E.

Stmt1: (x-1)^2 + (A-1) > 0. Insufficient. A can be positive or negative.

Stmt2: Ax^2 + 1 > 0. Insuffcient. A can be positive or negative.

Together also, insufficient.
Senior Manager
Joined: 18 Jun 2007
Posts: 274
Re: DS: A positive [#permalink]

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18 Oct 2008, 13:48
OA is not E.
Anymore guess before I disclose the OA?
Retired Moderator
Joined: 05 Jul 2006
Posts: 1734
Re: DS: A positive [#permalink]

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18 Oct 2008, 14:25
rishi2377 wrote:
Is A positive?
1. x^2-2*x+A is positive for all x
2. A*x^2+1 is positive for all x

x^2 -2*x+A = x^2 -2x-2A>0

2A< X^2 - 2X IE: 2A<X(X-2)........INSUFF

FROM 2

X^2 +1>0 THUS IF A*X^2 +1 > 0 THEN A is +ve

B
Current Student
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Re: DS: A positive [#permalink]

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18 Oct 2008, 15:20
i too get E..

what is the source of this question??

yess..what if A=-1/(infiniti)???? such that AX^2 is always less than 1...
VP
Joined: 17 Jun 2008
Posts: 1288
Re: DS: A positive [#permalink]

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18 Oct 2008, 23:20
rishi2377 wrote:
Is A positive?
1. x^2-2*x+A is positive for all x
2. A*x^2+1 is positive for all x

The questioin is not clear !!!

1) is insufficient since
x(x-2)>-A With different x A changes

if we say CASE1
1. x^2-2*x+A is positive for all x INSUFFI
2. A*(x^2)+1 is positive for all x SUFFI
different result !!!
else if we say CASE 2
1. x^2-2*x+A is positive for all x INSUFFI
2. (A*x)^2+1 is positive for all x INSUFFI
different result !!!

in second case CASE2 above ,(2) is INSUFFI since A can be +ve or -ve

In case1 ,(2) is SUFFI ,A needs to be +ve -ve value cannot suffice !!
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Senior Manager
Joined: 18 Jun 2007
Posts: 274
Re: DS: A positive [#permalink]

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19 Oct 2008, 11:59
Still not even a one correct answer.
Okay OA is A.

And the OE is
St1. can be rewritten as (x-1)^2 + A-1>0, for this to hold true for all possible values of x, A > 1. So sufficient.

What I didn't get is can we minus 1 from both parts of the equation??

Can anybody explain?
Senior Manager
Joined: 21 Apr 2008
Posts: 457
Schools: Kellogg, MIT, Michigan, Berkeley, Marshall, Mellon
Re: DS: A positive [#permalink]

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19 Oct 2008, 12:06
rishi2377 wrote:
Still not even a one correct answer.
Okay OA is A.

And the OE is
St1. can be rewritten as (x-1)^2 + A-1>0, for this to hold true for all possible values of x, A > 1. So sufficient.

What I didn't get is can we minus 1 from both parts of the equation??

Can anybody explain?

I'm afraid I don't understand the OE...

Let's take x=1, thus A>1
Let's take x=-1, thus A>-3, which includes negative values for A...

IMO: the answer should be E

What is the source of this question?

Cheers
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Senior Manager
Joined: 18 Jun 2007
Posts: 274
Re: DS: A positive [#permalink]

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19 Oct 2008, 13:33
John, I find this question in a former GMAT club member's notes
Yup me too didn't get it.
Senior Manager
Joined: 21 Apr 2008
Posts: 457
Schools: Kellogg, MIT, Michigan, Berkeley, Marshall, Mellon
Re: DS: A positive [#permalink]

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19 Oct 2008, 13:41
rishi2377 wrote:
John, I find this question in a former GMAT club member's notes
Yup me too didn't get it.

OK, I see...

Nevertheless, the OA cannot be A...

any explanation?

Cheers
_________________

mates, please visit my profile and leave comments
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I'm not linked to GMAT questions anymore, so, if you need something, please PM me

I'm already focused on my application package

My experience in my second attempt
http://gmatclub.com/forum/p544312#p544312
My experience in my third attempt
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VP
Joined: 17 Jun 2008
Posts: 1479
Re: DS: A positive [#permalink]

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19 Oct 2008, 21:55
rishi2377 wrote:
Still not even a one correct answer.
Okay OA is A.

And the OE is
St1. can be rewritten as (x-1)^2 + A-1>0, for this to hold true for all possible values of x, A > 1. So sufficient.

What I didn't get is can we minus 1 from both parts of the equation??

Can anybody explain?

What is the source of question. I completely disgree with the OE.

Take an example here.

x = 5 and A = -2 and still, (x-1)^2 + A-1 > 0
or x = 5 and A = 2 and still (x-1)^2 + A-1 > 0
SVP
Joined: 29 Aug 2007
Posts: 2427
Re: DS: A positive [#permalink]

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20 Oct 2008, 11:16
rishi2377 wrote:
Is A positive?

1. x^2-2*x+A is positive for all x
2. A*x^2+1 is positive for all x

Remember for all x!!!

In statement 1, can anybody prove that A is -ve if 0 < x < 2?

Therefore A.
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Manager
Joined: 23 Aug 2008
Posts: 62
Re: DS: A positive [#permalink]

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21 Oct 2008, 06:09
GMAT TIGER wrote:
rishi2377 wrote:
Is A positive?

1. x^2-2*x+A is positive for all x
2. A*x^2+1 is positive for all x

Remember for all x!!!

In statement 1, can anybody prove that A is -ve if 0 < x < 2?

Therefore A.

Hi, why are you limiting to 0<x<2?

My solution.
1) simplifies to A>x(2-x). A is +ve for any value 0<x<2; and could be +ve or -ve for all other values. Insufficient.
2) simplifies to A > -1/(x^2); A can be +ve or -ve for any value of x (except for x=0); therefore Insufficient.
1 and 2 together also insufficient, e.g. at x=3, (1) gives A>-3 and (2) gives A>-1/9; therefore A could still be either -ve or +ve; Answer E

PS I'm not sure if this helps visualize, as I don't know how to explain it ... I see (1) as an parabola cutting x axis at 0 and 2, center at 1,1; and (2) as a kind of hyperbola below the x axis.
SVP
Joined: 29 Aug 2007
Posts: 2427
Re: DS: A positive [#permalink]

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21 Oct 2008, 07:44
Every one who are sticking with E is missing my point. Try to understand what exactly meant by "for all x ". You never agree with me on OA (as A) if you keep on missing this statement: "for all x ".

If A is +ve, that value works for all x.
If A is -ve, that value doesnot work for all x.

Therefore A must be +ve.

If any, will clearify again.
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Retired Moderator
Joined: 18 Jul 2008
Posts: 902
Re: DS: A positive [#permalink]

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21 Oct 2008, 07:55
Some examples will help.

Thanks GMAT Tiger

GMAT TIGER wrote:
Every one who are sticking with E is missing my point. Try to understand what exactly meant by "for all x ". You never agree with me on OA (as A) if you keep on missing this statement: "for all x ".

If A is +ve, that value works for all x.
If A is -ve, that value doesnot work for all x.

Therefore A must be +ve.

If any, will clearify again.
SVP
Joined: 29 Aug 2007
Posts: 2427
Re: DS: A positive [#permalink]

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21 Oct 2008, 08:25
bigfernhead wrote:
Some examples will help.

Thanks GMAT Tiger

GMAT TIGER wrote:
Every one who are sticking with E is missing my point. Try to understand what exactly meant by "for all x ". You never agree with me on OA (as A) if you keep on missing this statement: "for all x ".

If A is +ve, that value works for all x.
If A is -ve, that value doesnot work for all x.

Therefore A must be +ve.

If any, will clearify again.

from statement 1:

(x^2 - 2x + A) > 0
(x^2 - 2x +1) + (A -1) > 0
(x-1)^2 + (A -1) > 0

suppose if x = 1, the inequality becomes: (A -1) > 0. so A has to be >1 to satisfy the inequality. Therefore A must be +ve.

The easiest way to understand this problem is that "when 1 > x > -1, A must be positive; when x>1 but <-1, A can either be positive or negative. Therefore the value of A has to be +ve for all values of x. Hence A is positive

I think statement 2 is not a disputable..

Hope that helps.

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If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: DS: A positive   [#permalink] 21 Oct 2008, 08:25
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# Is A positive? 1. x^2-2*x+A is positive for all x 2. A*x^2+1

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