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Director
Joined: 30 Nov 2006
Posts: 591
Location: Kuwait




SVP
Joined: 01 May 2006
Posts: 1796

Mishari wrote:
A it is .... Yes
It was to your question I said (E)



Director
Joined: 14 Jan 2007
Posts: 774

I got it, thanks Mishari for your patience.



Senior Manager
Joined: 04 Mar 2007
Posts: 434

How can it be A?
x^22*x + A>0
A>2*xx^2
assume x=1
A>21
A>1 > A is positiv
assume x=3
A>69
A>3
A might be 2, 1, 0 1 and so on...
So (1) is insuff
correct me please



Director
Joined: 30 Nov 2006
Posts: 591
Location: Kuwait

You know what guys .. I was trying to remember and think how I got A as an answer .. I failed !!!!!!!
I read my own explaination, it makes no sense to me !!!!!!!!
OH My God ! help
Depending on the value of X, A can be either positive or negative. Nothing is said about whether x is an integer or not.
When 0<x<1> A is positive
when 1<x<0> A could be negative or positive
For either case, the result of the equation is positive
MY UPDATED ANSWER: E
I disagree with the OA

Fig .. hmmm
I ... you know .. I really .. it's just that ..
aah well .. can you tell me how you got A for an answer ?



Senior Manager
Joined: 04 Mar 2007
Posts: 434

ok..Now I will try to get A
x^22*x +A is a parabola
x^22*x +A >0 as it is given in (1)
it means that for every given x, y>0
here we have a min point
min point of a parabola has coordinates [b/(2a); c(b^2/(4a))] > (1;A1)
ycoord of min point of this parabola = A1
ycoord must be > 0
A1>0
A>1
A  positive
I don't know
I am lost



SVP
Joined: 01 May 2006
Posts: 1796

Mishari wrote: You know what guys .. I was trying to remember and think how I got A as an answer .. I failed !!!!!!! I read my own explaination, it makes no sense to me !!!!!!!! OH My God ! help Depending on the value of X, A can be either positive or negative. Nothing is said about whether x is an integer or not. When 0<x<1> A is positive when 1<x<0> A could be negative or positive For either case, the result of the equation is positive MY UPDATED ANSWER: E I disagree with the OA  Fig .. hmmm I ... you know .. I really .. it's just that .. aah well .. can you tell me how you got A for an answer ?
It's by using the curves
y = a*(x  x1)*(xx2)
o If x < x1 or x > x2, then y will be of the sign of a
o If x1 < x < x2, then y will be of the sign of a
but,
In case of no root exists : b^2  4*a*c < 0, y will all time be of the sign of a from y = a*x^2 + b*x + c.
So, here, we search the value A for which 4 4*1*A < 0. That gives us A > 1 > 0.



Director
Joined: 14 Jan 2007
Posts: 774

My approach:
Stmt1: x^2  2x + A > 0
x^2  2x can be +ve or ve.
Here the ve value of if x^2  2x is the deciding factor value of A
if x^2  2x is ve, the least value x^2  2x can have is 1.
So A should be +ve.
Stmt2: A*x^2 + 1 > 0
for the above expression to be +ve for all x. A should be greater than or equal to zero. So INSUFF.
Hence the answer is A.



Director
Joined: 29 Aug 2005
Posts: 500

Let's look at stmt 1 : x^2  2*x + A
Put X = 0 , A>0 .
Put X = 1, 1+2+A>0 therefore A>3, does not prove conclusively.
Put X = 1 , 12+A>0 A1>0, A>1, therefore A>0
Statement 1 is not sufficent.
Let's look at stmt 2 : A*x^2 + 1 is positive for all x
Put X = 0 , A*0 + 1 >0, does not prove anything. A can be any value
Put X =1 , A*1+ 1 >0, A+1<0>1
Statement 2 is not sufficent.
Hence E should be the answer.
Last edited by vc019 on 12 Jun 2007, 20:04, edited 1 time in total.



GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

St1:
A must be at least 1. negative values of x poses no problems, but for values of x like 1 or 2, A must be positive in order for the function to stay positive. Sufficient.
St2:
Sufficient. If A is negative, then A*x^2 1 would not be positive for all x.
E.g. if x = 9, and A = 1, then Ax^2+1 = 8.
Ans: D



SVP
Joined: 01 May 2006
Posts: 1796

ywilfred wrote: St1: A must be at least 1. negative values of x poses no problems, but for values of x like 1 or 2, A must be positive in order for the function to stay positive. Sufficient.
St2: Sufficient. If A is negative, then A*x^2 1 would not be positive for all x. E.g. if x = 9, and A = 1, then Ax^2+1 = 8.
Ans: D
In stat 2, A could be equal to 0 : 0*x^2 + 1 = 1 > 0 ... I have fallen in the trap too



Manager
Joined: 17 Oct 2006
Posts: 52

Little help here plz. I too think that A cannot be the answer. I surely dont know about parabolas or curves yet, so i have decided to adopt the strategy of picking numbers. i have decided to pick 3 simple number 0,1,1 and when plug them into statement 1. for 0 and +1, A>0 but for 1, A >1/2, which shows that it is not sufficeint. If u could please explain this paradox and explain how it sufficient in simple words.
Also, Fig due, if u could please tell us all about curves and parabolas stuff or perhaps upload o document or a link where we can find details about this stuff, that will be a great help.



GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

Fig wrote: ywilfred wrote: St1: A must be at least 1. negative values of x poses no problems, but for values of x like 1 or 2, A must be positive in order for the function to stay positive. Sufficient.
St2: Sufficient. If A is negative, then A*x^2 1 would not be positive for all x. E.g. if x = 9, and A = 1, then Ax^2+1 = 8.
Ans: D In stat 2, A could be equal to 0 : 0*x^2 + 1 = 1 > 0 ... I have fallen in the trap too
ah yes... then it shoud be A



Director
Joined: 26 Feb 2006
Posts: 899

Re: DS: Is A +ve? [#permalink]
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13 Jun 2007, 00:26
Himalayan 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
I still think it should be E. It was discussed earlier and posted OE as under:
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.



GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

Re: DS: Is A +ve? [#permalink]
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13 Jun 2007, 00:38
Himalayan wrote: Himalayan 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 I still think it should be E. It was discussed earlier and posted OE as under: 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.
so if it's sufficient, how can it still be E? E
E  neither statement is sufficient to answer the question.



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Joined: 01 May 2006
Posts: 1796

Re: DS: Is A +ve? [#permalink]
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13 Jun 2007, 00:38
Himalayan wrote: Himalayan 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 I still think it should be E. It was discussed earlier and posted OE as under: 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.
The OE is right : this approach is excellent too
We know that (x1)^2 >= 0. Thus, to be sure that (x  1)^2 + A – 1 > 0, we need to have A  1 > 0 <=> A > 1.
Indeed, we take the minimum of (x1)^2 said 0 here and we plug it in the inequation:
0 + (A  1) > 0
<=> A > 1



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Re: DS: Is A +ve? [#permalink]
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13 Jun 2007, 00:40
ywilfred wrote: Himalayan wrote: Himalayan 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 I still think it should be E. It was discussed earlier and posted OE as under: 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. so if it's sufficient, how can it still be E? E E  neither statement is sufficient to answer the question.
I think Himalayan disagree with the OA



Intern
Joined: 11 Sep 2006
Posts: 47

Can some explain me
why do you say this?
From 1
x^2  2*x + A > 0
Meaning that :
b^2  4*a*c < 0 (this is the descriminat of a*x^2 + b*x + c)
How do you know that it has no real solution?



SVP
Joined: 01 May 2006
Posts: 1796

ajisha wrote: Can some explain me why do you say this?
From 1 x^2  2*x + A > 0 Meaning that : b^2  4*a*c < 0 (this is the descriminat of a*x^2 + b*x + c)
How do you know that it has no real solution?
We want to keep for all x : x^2  2*x + A > 0.
If b^2  4*a*c < 0, we have Sign(a*x^2+b*x+c) = Sign(a). So, the sign will not flip between roots cause there is no root (the curve stays on y>0 if a>0 or the curve stays on y <0 if a<0)
Hope that helps



GMAT Instructor
Joined: 04 Jul 2006
Posts: 1262
Location: Madrid

Re: DS: Is A +ve? [#permalink]
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01 Nov 2007, 04:24
Himalayan 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
1. y=(x1)^2 +(A1) >0
If A is not positive, y could be as small as A  1, which would be negative.
Thus A must be positive
SUFF
2 A must be positive or 0. NOT SUFF







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