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Is A positive? 1. x^22*x+A is positive for all x 2. A*x^2+1 [#permalink]
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17 Oct 2008, 10:04
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Is A positive? 1. x^22*x+A is positive for all x 2. A*x^2+1 is positive for all x



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Re: DS: A positive [#permalink]
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17 Oct 2008, 11:05
E.
Stmt1: (x1)^2 + (A1) > 0. Insufficient. A can be positive or negative.
Stmt2: Ax^2 + 1 > 0. Insuffcient. A can be positive or negative.
Together also, insufficient.



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Re: DS: A positive [#permalink]
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18 Oct 2008, 12:48
OA is not E. Anymore guess before I disclose the OA?



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Re: DS: A positive [#permalink]
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18 Oct 2008, 13:25
rishi2377 wrote: Is A positive? 1. x^22*x+A is positive for all x 2. A*x^2+1 is positive for all x x^2 2*x+A = x^2 2x2A>0 2A< X^2  2X IE: 2A<X(X2)........INSUFF FROM 2 X^2 +1>0 THUS IF A*X^2 +1 > 0 THEN A is +ve B



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Re: DS: A positive [#permalink]
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18 Oct 2008, 14:20
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...



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Re: DS: A positive [#permalink]
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18 Oct 2008, 22:20
rishi2377 wrote: Is A positive? 1. x^22*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(x2)>A With different x A changes if we say CASE1 1. x^22*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^22*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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Re: DS: A positive [#permalink]
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19 Oct 2008, 10:59
Still not even a one correct answer. Okay OA is A.
And the OE is St1. can be rewritten as (x1)^2 + A1>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?



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Re: DS: A positive [#permalink]
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19 Oct 2008, 11:06
rishi2377 wrote: Still not even a one correct answer. Okay OA is A.
And the OE is St1. can be rewritten as (x1)^2 + A1>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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Re: DS: A positive [#permalink]
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19 Oct 2008, 12:33
John, I find this question in a former GMAT club member's notes Yup me too didn't get it.



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Re: DS: A positive [#permalink]
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19 Oct 2008, 12:41
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
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Re: DS: A positive [#permalink]
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19 Oct 2008, 20:55
rishi2377 wrote: Still not even a one correct answer. Okay OA is A.
And the OE is St1. can be rewritten as (x1)^2 + A1>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, (x1)^2 + A1 > 0 or x = 5 and A = 2 and still (x1)^2 + A1 > 0



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Re: DS: A positive [#permalink]
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20 Oct 2008, 10:16
rishi2377 wrote: Is A positive?
1. x^22*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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Re: DS: A positive [#permalink]
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21 Oct 2008, 05:09
GMAT TIGER wrote: rishi2377 wrote: Is A positive?
1. x^22*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(2x). 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.



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Re: DS: A positive [#permalink]
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21 Oct 2008, 06:44
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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Re: DS: A positive [#permalink]
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21 Oct 2008, 06:55
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.



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Re: DS: A positive [#permalink]
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21 Oct 2008, 07:25
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 (x1)^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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