Author 
Message 
Senior Manager
Joined: 18 Jun 2007
Posts: 274

Is A positive? 1. x^22*x+A is positive for all x 2. A*x^2+1 [#permalink]
Show Tags
17 Oct 2008, 11:04
Question Stats:
0% (00:00) correct 0% (00:00) wrong based on 0 sessions
HideShow timer Statistics
Is A positive? 1. x^22*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 repost 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]
Show Tags
17 Oct 2008, 12:05
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.



Senior Manager
Joined: 18 Jun 2007
Posts: 274

Re: DS: A positive [#permalink]
Show Tags
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]
Show Tags
18 Oct 2008, 14:25
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



Current Student
Joined: 28 Dec 2004
Posts: 3292
Location: New York City
Schools: Wharton'11 HBS'12

Re: DS: A positive [#permalink]
Show Tags
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]
Show Tags
18 Oct 2008, 23:20
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 !!
_________________
cheers Its Now Or Never



Senior Manager
Joined: 18 Jun 2007
Posts: 274

Re: DS: A positive [#permalink]
Show Tags
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 (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?



Senior Manager
Joined: 21 Apr 2008
Posts: 457
Schools: Kellogg, MIT, Michigan, Berkeley, Marshall, Mellon

Re: DS: A positive [#permalink]
Show Tags
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 (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
_________________
mates, please visit my profile and leave comments http://gmatclub.com/forum/johnlewis1980sprofilefeedbackismorethanwelcome80538.html
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 http://gmatclub.com/forum/630q47v28engineernonnativespeakermyexperience78215.html#p588275



Senior Manager
Joined: 18 Jun 2007
Posts: 274

Re: DS: A positive [#permalink]
Show Tags
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]
Show Tags
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 http://gmatclub.com/forum/johnlewis1980sprofilefeedbackismorethanwelcome80538.html
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 http://gmatclub.com/forum/630q47v28engineernonnativespeakermyexperience78215.html#p588275



VP
Joined: 17 Jun 2008
Posts: 1479

Re: DS: A positive [#permalink]
Show Tags
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 (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



SVP
Joined: 29 Aug 2007
Posts: 2427

Re: DS: A positive [#permalink]
Show Tags
20 Oct 2008, 11:16
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.
_________________
Verbal: http://gmatclub.com/forum/newtotheverbalforumpleasereadthisfirst77546.html Math: http://gmatclub.com/forum/newtothemathforumpleasereadthisfirst77764.html Gmat: http://gmatclub.com/forum/everythingyouneedtoprepareforthegmatrevised77983.html
GT



Manager
Joined: 23 Aug 2008
Posts: 62

Re: DS: A positive [#permalink]
Show Tags
21 Oct 2008, 06:09
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.



SVP
Joined: 29 Aug 2007
Posts: 2427

Re: DS: A positive [#permalink]
Show Tags
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.
_________________
Verbal: http://gmatclub.com/forum/newtotheverbalforumpleasereadthisfirst77546.html Math: http://gmatclub.com/forum/newtothemathforumpleasereadthisfirst77764.html Gmat: http://gmatclub.com/forum/everythingyouneedtoprepareforthegmatrevised77983.html
GT



Retired Moderator
Joined: 18 Jul 2008
Posts: 902

Re: DS: A positive [#permalink]
Show Tags
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]
Show Tags
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 (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. == Message from GMAT Club Team == This is not a quality discussion. It has been retired. If you would like to discuss this question please repost 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.
_________________
Verbal: http://gmatclub.com/forum/newtotheverbalforumpleasereadthisfirst77546.html Math: http://gmatclub.com/forum/newtothemathforumpleasereadthisfirst77764.html Gmat: http://gmatclub.com/forum/everythingyouneedtoprepareforthegmatrevised77983.html
GT




Re: DS: A positive
[#permalink]
21 Oct 2008, 08:25






