It is currently 24 Nov 2017, 06:41

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Senior Manager
Senior Manager
avatar
Joined: 05 Oct 2008
Posts: 267

Kudos [?]: 550 [0], given: 22

Is A positive? 1. x^2 - 2x + A is positive for all x 2. Ax^2 [#permalink]

Show Tags

New post 06 Nov 2008, 05:54
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Is \(A\) positive?

1. \(x^2 - 2x + A\) is positive for all \(x\)
2. \(Ax^2 + 1\) is positive for all \(x\)

Please provide an explanation to your answers

Kudos [?]: 550 [0], given: 22

SVP
SVP
User avatar
Joined: 29 Aug 2007
Posts: 2471

Kudos [?]: 857 [0], given: 19

Re: No. Properties [#permalink]

Show Tags

New post 06 Nov 2008, 08:40
study wrote:
Is \(A\) positive?

1. \(x^2 - 2x + A\) is positive for all \(x\)
2. \(Ax^2 + 1\) is positive for all \(x\)

Please provide an explanation to your answers


It is one of the most difficult one to grasp. It was discussed just a while ago.

Go though this and then comeback with your doubts: 7-p530279?t=71816#p530279
_________________

Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html
Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

Kudos [?]: 857 [0], given: 19

SVP
SVP
User avatar
Joined: 29 Aug 2007
Posts: 2471

Kudos [?]: 857 [0], given: 19

Re: No. Properties [#permalink]

Show Tags

New post 06 Nov 2008, 22:36
GMAT TIGER wrote:
study wrote:
Is \(A\) positive?

1. \(x^2 - 2x + A\) is positive for all \(x\)
2. \(Ax^2 + 1\) is positive for all \(x\)

Please provide an explanation to your answers


It is one of the most difficult one to grasp. It was discussed just a while ago.

Go though this and then comeback with your doubts: 7-p530279?t=71816#p530279


No more takers?

its really intreasting!!!!!!!!! 8-) 8-) 8-)
_________________

Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html
Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

Kudos [?]: 857 [0], given: 19

SVP
SVP
avatar
Joined: 17 Jun 2008
Posts: 1534

Kudos [?]: 280 [0], given: 0

Re: No. Properties [#permalink]

Show Tags

New post 06 Nov 2008, 23:05
GMAT TIGER wrote:
No more takers?

its really intreasting!!!!!!!!! 8-) 8-) 8-)


Although I had answered E in the previous post, after re-visiting the question, I will go with D. "for all x" is important here.

From stmt1: {m}(x-1)^2 + (A-1) > 0 {/m} for all x and this is possible only when A-1> or A > 1 or A is positive. Sufficient.

From stmt2: A has to be positive as x^2 is positive. Sufficient.

Kudos [?]: 280 [0], given: 0

SVP
SVP
User avatar
Joined: 29 Aug 2007
Posts: 2471

Kudos [?]: 857 [0], given: 19

Re: No. Properties [#permalink]

Show Tags

New post 06 Nov 2008, 23:30
scthakur wrote:
GMAT TIGER wrote:
No more takers?

its really intreasting!!!!!!!!! 8-) 8-) 8-)


Although I had answered E in the previous post, after re-visiting the question, I will go with D. "for all x" is important here.

From stmt1: {m}(x-1)^2 + (A-1) > 0 {/m} for all x and this is possible only when A-1> or A > 1 or A is positive. Sufficient.

From stmt2: A has to be positive as x^2 is positive. Sufficient.


2. Ax^2 + 1 is positive for all x.

What if in statement 2: (1) x = 0.5, A = 1 and (2) x = 0.5, A = -1?
_________________

Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html
Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

Kudos [?]: 857 [0], given: 19

SVP
SVP
avatar
Joined: 17 Jun 2008
Posts: 1534

Kudos [?]: 280 [0], given: 0

Re: No. Properties [#permalink]

Show Tags

New post 06 Nov 2008, 23:42
GMAT TIGER wrote:
2. Ax^2 + 1 is positive for all x.

What if in statement 2: (1) x = 0.5, A = 1 and (2) x = 0.5, A = -1?



It is "for all x". Hence, A has to be positive for all x. For x = 0.5, A can be negative , but for x = 50, it cannot be. For all values of x, if A is positive, the inequality will hold good.

Kudos [?]: 280 [0], given: 0

SVP
SVP
User avatar
Joined: 29 Aug 2007
Posts: 2471

Kudos [?]: 857 [0], given: 19

Re: No. Properties [#permalink]

Show Tags

New post 07 Nov 2008, 00:00
scthakur wrote:
GMAT TIGER wrote:
2. Ax^2 + 1 is positive for all x.

What if in statement 2: (1) x = 0.5, A = 1 and (2) x = 0.5, A = -1?



It is "for all x". Hence, A has to be positive for all x. For x = 0.5, A can be negative , but for x = 50, it cannot be. For all values of x, if A is positive, the inequality will hold good.


exactly. here A doesnot need to be +ve to have (Ax^2 + 1) > 0.

With -ve and +ve values for A, (Ax^2 + 1) has to be +ve but not necessarily A.
_________________

Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html
Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

Kudos [?]: 857 [0], given: 19

SVP
SVP
avatar
Joined: 17 Jun 2008
Posts: 1534

Kudos [?]: 280 [0], given: 0

Re: No. Properties [#permalink]

Show Tags

New post 07 Nov 2008, 02:15
GMAT TIGER wrote:
exactly. here A doesnot need to be +ve to have (Ax^2 + 1) > 0.

With -ve and +ve values for A, (Ax^2 + 1) has to be +ve but not necessarily A.


I will begin with stmt1.

From stmt1: (x-1)^2 + (A-1) > 0
Here, (x-1)^2 is positive for all X. And, A can be positive or negative for the expression to be true.

For example, x = 0.5, A = 1.
or, x = 5, A = -10
Both the cases will satisfy the ineuqality. However, for certain x, A can be +ve or -ve, but for some other x, A has to be +ve. That means, A must be positive for all x.

From stmt2: Ax^2 + 1 > 0
Here, second expression is positive and x^2 is positive. Hence, A can be positive or negative for certain x and only positive for other x.
For example, for x = 0.5, A can be -1 or +1.
but, for x = 5, A has to be +1 only.
But, positive value of A will satisfy all values of x and not the negative value.

Kudos [?]: 280 [0], given: 0

SVP
SVP
User avatar
Joined: 29 Aug 2007
Posts: 2471

Kudos [?]: 857 [0], given: 19

Re: No. Properties [#permalink]

Show Tags

New post 07 Nov 2008, 09:19
scthakur wrote:
GMAT TIGER wrote:
exactly. here A doesnot need to be +ve to have (Ax^2 + 1) > 0.

With -ve and +ve values for A, (Ax^2 + 1) has to be +ve but not necessarily A.


I will begin with stmt1.

From stmt1: (x-1)^2 + (A-1) > 0
Here, (x-1)^2 is positive for all X. And, A can be positive or negative for the expression to be true.

For example, x = 0.5, A = 1.
or, x = 5, A = -10
Both the cases will satisfy the ineuqality. However, for certain x, A can be +ve or -ve, but for some other x, A has to be +ve. That means, A must be positive for all x.

From stmt2: Ax^2 + 1 > 0
Here, second expression is positive and x^2 is positive. Hence, A can be positive or negative for certain x and only positive for other x.
For example, for x = 0.5, A can be -1 or +1.
but, for x = 5, A has to be +1 only.
But, positive value of A will satisfy all values of x and not the negative value.


I thik it would be better if we say A can be +ve or 0.

I agree with you that A cannot be -ve.
_________________

Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html
Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT

Kudos [?]: 857 [0], given: 19

Current Student
avatar
Joined: 28 Dec 2004
Posts: 3345

Kudos [?]: 323 [0], given: 2

Location: New York City
Schools: Wharton'11 HBS'12
Re: No. Properties [#permalink]

Show Tags

New post 07 Nov 2008, 09:59
i agree A is the ans..

stmnt 1: x^2-2x+1+A-1

(x-1)^2 + (A-1)>0 so for all x; if x=0 then its clear A>0

Kudos [?]: 323 [0], given: 2

SVP
SVP
avatar
Joined: 17 Jun 2008
Posts: 1534

Kudos [?]: 280 [0], given: 0

Re: No. Properties [#permalink]

Show Tags

New post 07 Nov 2008, 11:37
study, do you have the OA and OE (if any) please?

Kudos [?]: 280 [0], given: 0

Re: No. Properties   [#permalink] 07 Nov 2008, 11:37
Display posts from previous: Sort by

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

  post reply Question banks Downloads My Bookmarks Reviews Important topics  

Moderator: chetan2u



GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.