Find all School-related info fast with the new School-Specific MBA Forum

It is currently 11 Jul 2014, 03:48

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
2 KUDOS received
SVP
SVP
avatar
Joined: 16 Jul 2009
Posts: 1634
Schools: CBS
WE 1: 4 years (Consulting)
Followers: 30

Kudos [?]: 193 [2] , given: 2

GMAT Tests User
Is A positive? x^2-2x+A is positive for all x Ax^2+1 is [#permalink] New post 15 Jul 2010, 11:42
2
This post received
KUDOS
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

24% (02:43) correct 75% (06:47) wrong based on 352 sessions
Is A positive?

(1) x^2-2x+A is positive for all x
(2) Ax^2+1 is positive for all x
[Reveal] Spoiler: OA

_________________

The sky is the limit
800 is the limit


Get the best GMAT Prep Resources with GMAT Club Premium Membership


Last edited by Bunuel on 10 Apr 2012, 23:06, edited 1 time in total.
Edited the question
Expert Post
8 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18492
Followers: 3188

Kudos [?]: 21234 [8] , given: 2537

Re: Is A positive? [#permalink] New post 15 Jul 2010, 13:40
8
This post received
KUDOS
Expert's post
noboru wrote:
Is A positive?

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


OA is A


Is A>0?

(1) x^2-2x+A is positive for all x:

Quadratic expression x^2-2x+A is a function of of upward parabola (it's upward as coefficient of x^2 is positive). We are told that this expression is positive for all x --> x^2-2x+A>0, which means that this parabola is "above" X-axis OR in other words parabola has no intersections with X-axis OR equation x^2-2x+A=0 has no real roots.

Quadratic equation to has no real roots discriminant must be negative --> D=2^2-4A=4-4A<0 --> 1-A<0 --> A>1.

Sufficient.

(2) Ax^2+1 is positive for all x:

Ax^2+1>0 --> when A\geq0 this expression is positive for all x. So A can be zero too.

Not sufficient.

Answer: A.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 22 Jun 2010
Posts: 57
Followers: 1

Kudos [?]: 6 [0], given: 10

Re: Is A positive? [#permalink] New post 16 Jul 2010, 04:21
Hi,

I dont get it sorry... I mean I understand your equations Bunuel, but I tried first with picking numbers:

If I pick -0.5 for x --> x^2-2x+A>0 will hold for A > -1.25

...

Where is my mistake??
Expert Post
6 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18492
Followers: 3188

Kudos [?]: 21234 [6] , given: 2537

Re: Is A positive? [#permalink] New post 16 Jul 2010, 07:01
6
This post received
KUDOS
Expert's post
AndreG wrote:
Hi,

I dont get it sorry... I mean I understand your equations Bunuel, but I tried first with picking numbers:

If I pick -0.5 for x --> x^2-2x+A>0 will hold for A > -1.25

...

Where is my mistake??


The point here is that x^2-2x+A>0 for all x-es.

Let's do this in another way:

We have (x^2-2x)+A>0 for all x-es. The sum of 2 quantities (x^2-2x and A) is positive for all x-es. So for the least value of x^2-2x, A must make the whole expression positive.

So what is the least value of x^2-2x? The least value of quadratic expression ax^2+bx+c is when x=-\frac{b}{2a}, so in our case the least value of x^2-2x is when x=-\frac{-2}{2}=1 --> x^2-2x=-1 --> -1+A>0 --> A>1.

OR:

x^2-2x+A>0 --> x^2-2x+1+A-1>0 --> (x-1)^2+A-1>0 --> least value of (x-1)^2 is zero thus A-1 must be positive (0+A-1>0)--> A-1>0 --> A>1.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 22 Jun 2010
Posts: 57
Followers: 1

Kudos [?]: 6 [0], given: 10

Re: Is A positive? [#permalink] New post 16 Jul 2010, 07:26
Wow u rock man! :-)
That was very clear!

I especially like the +1 -1 trick

Posted from my mobile device Image
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 25 Jun 2009
Posts: 313
Followers: 2

Kudos [?]: 67 [1] , given: 6

GMAT Tests User
Re: Is A positive? [#permalink] New post 16 Jul 2010, 08:36
1
This post received
KUDOS
Hi Bunuel,

I really liked approached here but I still have some confusion,

Say for e.g if try to pick the numbers say x = -3

Then the equation in the first statement becomes

x^2 - 2x + A = 9 +6 +A = 15 + A >0

So now if we see A can have -ve and +ve values, isnt it ?

I am confused with this.

Please explain, whats wrong with this one.

Cheers
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18492
Followers: 3188

Kudos [?]: 21234 [0], given: 2537

Re: Is A positive? [#permalink] New post 16 Jul 2010, 08:49
Expert's post
nitishmahajan wrote:
Hi Bunuel,

I really liked approached here but I still have some confusion,

Say for e.g if try to pick the numbers say x = -3

Then the equation in the first statement becomes

x^2 - 2x + A = 9 +6 +A = 15 + A >0

So now if we see A can have -ve and +ve values, isnt it ?

I am confused with this.

Please explain, whats wrong with this one.

Cheers


Not every question can be solved by number picking.

For all x-es means that no matter what x you pick x^2 - 2x + A must be positive. So it must be positive even for the lowest value of x^2 - 2x which is -1 --> so -1+A must be positive hence A must be more than 1.

Now again: if A>1 then for any x expression x^2 - 2x + A is positive.

But if A=-15 (or any other number less than 1) we can find some x-es for which expression x^2 - 2x + A is not positive, so theese values of A (values of A\leq{1}) are not valid.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 25 Jun 2009
Posts: 313
Followers: 2

Kudos [?]: 67 [0], given: 6

GMAT Tests User
Re: Is A positive? [#permalink] New post 16 Jul 2010, 08:56
Bunuel wrote:
nitishmahajan wrote:
Hi Bunuel,

I really liked approached here but I still have some confusion,

Say for e.g if try to pick the numbers say x = -3

Then the equation in the first statement becomes

x^2 - 2x + A = 9 +6 +A = 15 + A >0

So now if we see A can have -ve and +ve values, isnt it ?

I am confused with this.

Please explain, whats wrong with this one.

Cheers


Not every question can be solved by number picking.

For all x-es means that no matter what x you pick x^2 - 2x + A must be positive. So it must be positive even for the lowest value of x^2 - 2x which is -1 --> so -1+A must be positive hence A must be more than 1.

Now again: if A>1 then for any x expression x^2 - 2x + A is positive.

But if A=-15 (or any other number less than 1) we can find some x-es for which expression x^2 - 2x + A is not positive, so theese values of A (values of A\leq{1}) are not valid.

Hope it's clear.


Thanks for the reply Bunuel,

I understood the approach but the fact which is baffling me is that say the equation after subsituting value of x=-3 i.e 15+ A > 0 now we can have a value of A=-3 or may be -4 etc and still have the value of the equation in statement 1 as +ve

Am I thinking too much or just lacking some thing basic concept.

I appreciate your patience. :)
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18492
Followers: 3188

Kudos [?]: 21234 [0], given: 2537

Re: Is A positive? [#permalink] New post 16 Jul 2010, 09:16
Expert's post
nitishmahajan wrote:
Bunuel wrote:
nitishmahajan wrote:
Hi Bunuel,

I really liked approached here but I still have some confusion,

Say for e.g if try to pick the numbers say x = -3

Then the equation in the first statement becomes

x^2 - 2x + A = 9 +6 +A = 15 + A >0

So now if we see A can have -ve and +ve values, isnt it ?

I am confused with this.

Please explain, whats wrong with this one.

Cheers


Not every question can be solved by number picking.

For all x-es means that no matter what x you pick x^2 - 2x + A must be positive. So it must be positive even for the lowest value of x^2 - 2x which is -1 --> so -1+A must be positive hence A must be more than 1.

Now again: if A>1 then for any x expression x^2 - 2x + A is positive.

But if A=-15 (or any other number less than 1) we can find some x-es for which expression x^2 - 2x + A is not positive, so theese values of A (values of A\leq{1}) are not valid.

Hope it's clear.


Thanks for the reply Bunuel,

I understood the approach but the fact which is baffling me is that say the equation after subsituting value of x=-3 i.e 15+ A > 0 now we can have a value of A=-3 or may be -4 etc and still have the value of the equation in statement 1 as +ve

Am I thinking too much or just lacking some thing basic concept.

I appreciate your patience. :)


I think you just don't understand one thing in statement (1): x^2-2x+A>0 FOR ALL x-es.

You say that if x=-3 then A can be for example -10 (or any number more than -15) and x^2-2x+A will be positive, but if x=1 does A=-10 makes x^2-2x+A positive? NO!

So you should find such value of A (such range) for which x^2-2x+A is positive no matter what value of x you'll plug. And the way how to find this range is shown in my previous posts.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 25 Jun 2009
Posts: 313
Followers: 2

Kudos [?]: 67 [0], given: 6

GMAT Tests User
Re: Is A positive? [#permalink] New post 16 Jul 2010, 09:23
Thanks Bunuel,

Now I understood, :)

I appreciate your patience in making me understand this one ..!

Cheers,
1 KUDOS received
SVP
SVP
avatar
Joined: 16 Jul 2009
Posts: 1634
Schools: CBS
WE 1: 4 years (Consulting)
Followers: 30

Kudos [?]: 193 [1] , given: 2

GMAT Tests User
Re: Is A positive? [#permalink] New post 27 Jul 2010, 14:47
1
This post received
KUDOS
And all this has to come to me in less than 2 mins?
_________________

The sky is the limit
800 is the limit


Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 11 Feb 2011
Posts: 80
Followers: 1

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

DS: number properties [#permalink] New post 10 Apr 2012, 18:17
Is A positive?

1) X^2-2X+A is positive for all X
2) AX^2 + 1 is positive for all X

given answer as A...but i thought it should be E..
source: hard problems from gmatclub tests number properties I
SVP
SVP
avatar
Joined: 16 Nov 2010
Posts: 1692
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 30

Kudos [?]: 272 [0], given: 36

GMAT Tests User Premium Member Reviews Badge
Re: DS: number properties [#permalink] New post 10 Apr 2012, 20:03
1) X^2-2X+A is positive for all X
I think A could not be the answer, for example, if A = 0, and X = 4, then also the expression is positive, but A = 0 is neither positive nor negative
Again, if A = 1, and and X = 4, then also the expression is positive

2) AX^2 + 1 is positive for all X
Same logic as above, if A is 0, then the expression is positive, and the expression is also postive for any value of X where A > 0

In a nutshell, I too think the answer is E.

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4517
Location: Pune, India
Followers: 1012

Kudos [?]: 4310 [1] , given: 161

Re: DS: number properties [#permalink] New post 11 Apr 2012, 09:42
1
This post received
KUDOS
Expert's post
rongali wrote:
Is A positive?

1) X^2-2X+A is positive for all X
2) AX^2 + 1 is positive for all X

given answer as A...but i thought it should be E..
source: hard problems from gmatclub tests number properties I


1) X^2-2X+A is positive for all X

For all values of X,X^2-2X+A > 0
This means, for X = 0, X^2-2X+A > 0; for X = 1, X^2-2X+A > 0; for X = -2, X^2-2X+A > 0 etc etc etc

Let's put X = 0. 0^2-2*0+A > 0 should hold. Therefore, A > 0 should hold.
Sufficient.

2) AX^2 + 1 is positive for all X

For all X, AX^2 + 1 > 0
Here, A could be positive or A could be 0 (since, when A = 0, we get 1 > 0 which holds no matter what the value of X.)
Since A can be 0, we cannot say whether A is positive. Not Sufficient.

Answer A
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Intern
Intern
avatar
Joined: 25 Jun 2011
Posts: 49
Location: Sydney
Followers: 0

Kudos [?]: 1 [0], given: 7

GMAT Tests User
Re: Is A positive? [#permalink] New post 04 Jul 2012, 02:55
Bunuel wrote:
noboru wrote:
Is A positive?

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


OA is A


(2) Ax^2+1 is positive for all x:

Ax^2+1>0 --> when A\geq0 this expression is positive for all x. So A can be zero too.

Not sufficient.

Answer: A.


Why didn't you use the discriminant formula to assess statement 2?

I tried the discriminant rule and got a>0. I had 0-4a<0 which turns to a>0.

What am I missing here?

Thanks,
Diana
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18492
Followers: 3188

Kudos [?]: 21234 [0], given: 2537

Re: Is A positive? [#permalink] New post 04 Jul 2012, 02:59
Expert's post
dianamao wrote:
Bunuel wrote:
noboru wrote:
Is A positive?

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


OA is A


(2) Ax^2+1 is positive for all x:

Ax^2+1>0 --> when A\geq0 this expression is positive for all x. So A can be zero too.

Not sufficient.

Answer: A.


Why didn't you use the discriminant formula to assess statement 2?

I tried the discriminant rule and got a>0. I had 0-4a<0 which turns to a>0.

What am I missing here?

Thanks,
Diana


You are right: if we use the same approach for (2) then we'll get A>0 BUT if A=0 then Ax^2+1 won't be a quadratic function anymore. So this approach will work only if A doesn't equal to zero, but we can not eliminate this case and if A=0 then Ax^2+1=1 is also always positive. Hence Ax^2+1 is positive for A>0 (if we use quadratic function approach) as well as for A=0, so for A\geq0.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 09 Apr 2012
Posts: 5
Followers: 0

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

Is A positive? [#permalink] New post 19 Aug 2012, 18:11
This is a question from gmat club tests.

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

I got E and my way of solving is as below:
St1. x^2 - 2x +A > 0
Let x=0, so A>0. Let x=-1, so A>-3. In this case A can be negative or positive. Insufficient.

St2. A*x^2 +1 > 0
Let x=-1, so A>-1. Again A can be positive or negative. Insufficient.

St1+St2: Let x=-1, so A > -1. Again A can be positive or negative. Insufficient.

So it's E. However the OA is not E. Please advise.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18492
Followers: 3188

Kudos [?]: 21234 [0], given: 2537

Re: Is A positive? [#permalink] New post 20 Aug 2012, 00:36
Expert's post
shivamayam wrote:
This is a question from gmat club tests.

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

I got E and my way of solving is as below:
St1. x^2 - 2x +A > 0
Let x=0, so A>0. Let x=-1, so A>-3. In this case A can be negative or positive. Insufficient.

St2. A*x^2 +1 > 0
Let x=-1, so A>-1. Again A can be positive or negative. Insufficient.

St1+St2: Let x=-1, so A > -1. Again A can be positive or negative. Insufficient.

So it's E. However the OA is not E. Please advise.


Merging similar topics. Please refer to the solutions above.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Intern
Intern
User avatar
Joined: 12 Feb 2012
Posts: 38
Location: United States
GMAT Date: 08-30-2012
Followers: 0

Kudos [?]: 17 [1] , given: 15

Re: Is A positive? x^2-2x+A is positive for all x Ax^2+1 is [#permalink] New post 21 Aug 2012, 15:51
1
This post received
KUDOS
best way to deal this problem is to bet on A more than X..
it wud b yes if A>0 Or No ,if A<0 ....
then first assume A>0 , then check whether statement 1 & 2 is true or not for all value of X....
then assume A<0 ,then check whether statement 1 & 2 is true or not for all value of X....
_________________

KUMAR GAURAB
GET MAD ABOUT TEST

Intern
Intern
avatar
Joined: 21 Aug 2012
Posts: 27
Followers: 0

Kudos [?]: 4 [0], given: 4

Re: Is A positive? [#permalink] New post 21 Aug 2012, 18:57
dianamao wrote:
Bunuel wrote:
noboru wrote:
Is A positive?

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


OA is A


(2) Ax^2+1 is positive for all x:

Ax^2+1>0 --> when A\geq0 this expression is positive for all x. So A can be zero too.

Not sufficient.

Answer: A.


Why didn't you use the discriminant formula to assess statement 2?

I tried the discriminant rule and got a>0. I had 0-4a<0 which turns to a>0.

What am I missing here?

Thanks,
Diana


@Diana - Which discriminant rule did you use?
_________________

Please give kudos if you like my reply!

Re: Is A positive?   [#permalink] 21 Aug 2012, 18:57
    Similar topics Author Replies Last post
Similar
Topics:
7 Experts publish their posts in the topic If x, y, and z are all positive integers, what is the Maxswe 21 07 Nov 2012, 13:53
Is A positive? (1) x^2 - 2x + A is positive for all x (2) tarek99 8 26 Mar 2008, 05:01
Experts publish their posts in the topic Is A positive? 1. x^2 - 2x + A is positive for all x 2. bmwhype2 9 20 Dec 2007, 08:24
If all members of Set X are positive integers, what is the kevincan 6 09 Jul 2006, 03:29
If x represents the sum of all the positive three-digit saha 5 18 May 2006, 07:38
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page    1   2   3    Next  [ 47 posts ] 



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

Powered by phpBB © phpBB Group and phpBB SEO

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®.