Author 
Message 
TAGS:

Hide Tags

VP
Joined: 16 Jul 2009
Posts: 1192
Schools: CBS
WE 1: 4 years (Consulting)

Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
Updated on: 12 Apr 2018, 01:57
Question Stats:
32% (01:36) correct 68% (03:21) wrong based on 1157 sessions
HideShow timer Statistics
Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1 is positive for all x
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
The sky is the limit 800 is the limit
GMAT Club Premium Membership  big benefits and savings
Originally posted by noboru on 15 Jul 2010, 12:42.
Last edited by Bunuel on 12 Apr 2018, 01:57, edited 2 times in total.
Edited the question




Math Expert
Joined: 02 Sep 2009
Posts: 49303

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
15 Jul 2010, 14:40
noboru wrote: Is A positive?
x^22x+A is positive for all x Ax^2+1 is positive for all x
OA is A Is \(A>0\)? (1) \(x^22x+A\) is positive for all \(x\): Quadratic expression \(x^22x+A\) 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 \(x\) > \(x^22x+A>0\), which means that this parabola is "above" Xaxis OR in other words parabola has no intersections with Xaxis OR equation \(x^22x+A=0\) has no real roots. Quadratic equation to has no real roots discriminant must be negative > \(D=2^24A=44A<0\) > \(1A<0\) > \(A>1\). 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 the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics




Manager
Joined: 22 Jun 2010
Posts: 50

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
16 Jul 2010, 05:21
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^22x+A>0 will hold for A > 1.25
...
Where is my mistake??



Math Expert
Joined: 02 Sep 2009
Posts: 49303

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
16 Jul 2010, 08:01
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^22x+A>0 will hold for A > 1.25
...
Where is my mistake?? The point here is that \(x^22x+A>0\) for all \(xes\). Let's do this in another way: We have \((x^22x)+A>0\) for all \(xes\). The sum of 2 quantities (\(x^22x\) and \(A\)) is positive for all \(xes\). So for the least value of \(x^22x\), \(A\) must make the whole expression positive. So what is the least value of \(x^22x\)? The least value of quadratic expression \(ax^2+bx+c\) is when \(x=\frac{b}{2a}\), so in our case the least value of \(x^22x\) is when \(x=\frac{2}{2}=1\) > \(x^22x=1\) > \(1+A>0\) > \(A>1\). OR: \(x^22x+A>0\) > \(x^22x+1+A1>0\) > \((x1)^2+A1>0\) > least value of \((x1)^2\) is zero thus \(A1\) must be positive (\(0+A1>0\))> \(A1>0\) > \(A>1\). Hope it's clear.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 22 Jun 2010
Posts: 50

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
16 Jul 2010, 08:26
Wow u rock man! That was very clear! I especially like the +1 1 trick Posted from my mobile device



Senior Manager
Joined: 25 Jun 2009
Posts: 281

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
16 Jul 2010, 09:36
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



Math Expert
Joined: 02 Sep 2009
Posts: 49303

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
16 Jul 2010, 09:49
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 \(xes\) 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 \(xes\) 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 the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 25 Jun 2009
Posts: 281

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
16 Jul 2010, 09:56
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 \(xes\) 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 \(xes\) 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.



Math Expert
Joined: 02 Sep 2009
Posts: 49303

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
16 Jul 2010, 10:16
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 \(xes\) 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 \(xes\) 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): \(x^22x+A>0\) FOR ALL \(xes\). You say that if \(x=3\) then \(A\) can be for example 10 (or any number more than 15) and \(x^22x+A\) will be positive, \(but\) if \(x=1\) does \(A=10\) makes \(x^22x+A\) positive? NO! So you should find such value of \(A\) (such range) for which \(x^22x+A\) 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 the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8288
Location: Pune, India

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
11 Apr 2012, 10:42
rongali wrote: Is A positive? 1) X^22X+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^22X+A is positive for all X For all values of X,\(X^22X+A > 0\) This means, for X = 0, \(X^22X+A > 0\); for X = 1, \(X^22X+A > 0\); for X = 2, \(X^22X+A > 0\) etc etc etc Let's put X = 0. \(0^22*0+A > 0\) 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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 25 Jun 2011
Posts: 37
Location: Sydney

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
04 Jul 2012, 03:55
Bunuel wrote: noboru wrote: Is A positive?
x^22x+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 04a<0 which turns to a>0. What am I missing here? Thanks, Diana



Math Expert
Joined: 02 Sep 2009
Posts: 49303

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
04 Jul 2012, 03:59
dianamao wrote: Bunuel wrote: noboru wrote: Is A positive?
x^22x+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 04a<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 the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 12 Feb 2012
Posts: 32
Location: United States
GMAT Date: 08302012

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
21 Aug 2012, 16:51
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



Senior Manager
Joined: 07 Sep 2010
Posts: 281

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
19 May 2013, 00:51
Bunuel wrote: Quadratic expression \(x^22x+A\) 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 \(x\) > \(x^22x+A>0\), which means that this parabola is "above" Xaxis OR in other words parabola has no intersections with Xaxis OR equation \(x^22x+A=0\) has no real roots.
Hi Bunuel, How did you infer that the parabola would be above X axis by looking at the equation?? Pls explain. Regards, H



Math Expert
Joined: 02 Sep 2009
Posts: 49303

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
19 May 2013, 04:30



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8288
Location: Pune, India

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
24 Sep 2013, 20:44
VeritasPrepKarishma wrote: rongali wrote: Is A positive? 1) X^22X+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^22X+A is positive for all X For all values of X,\(X^22X+A > 0\) This means, for X = 0, \(X^22X+A > 0\); for X = 1, \(X^22X+A > 0\); for X = 2, \(X^22X+A > 0\) etc etc etc Let's put X = 0. \(0^22*0+A > 0\) 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 Responding to a pm: Quote: I still did not understand your solution x^22x+A>0 if we take the value 3 for example , 96+A>0 3+A>0 which gives A>()3 so A can assume 2,1,0 and so on and we still get the overall value as +ve. Can you help me understand what i am missing ? Given that x^22x+A is always positive. No matter what the value of x, the value of A is such that this expression is always positive. Whether x = ...2, 0, 1, 4, 100..., the expression will always be positive. So let's put a few values of x. Put x = 2 (2)^22(2)+A > 0 A > 8 Put x = 0 0^2  2*0 + A > 0 A > 0 Put x = 1 1^2  2*1 + A > 0 A > 1 Put x = 3 3^2  2*3 + A > 0 A > 3 and so on... So we see that A must be greater than 8, it should also be greater than 3, it should also be greater than 0 and it should also be greater than 1. So what values do you think A can take? Values which are greater than all these values i.e. values like 8, 10 etc. In any case, we are asked whether A is positive and we know that it must be greater than 1. Hence, we know that A must be positive. Sufficient.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 07 Aug 2012
Posts: 16

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
17 Oct 2013, 04:46
Dear Brunel
Please explain last line ....
We have (x^22x)+A>0 for all xes. The sum of 2 quantities (x^22x and A) is positive for all xes. So for the least value of x^22x, A must make the whole expression positive.
So what is the least value of x^22x? 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^22x is when x=\frac{2}{2}=1 > x^22x=1 > 1+A>0 > A>1. ....Want to know how +1 changes to 1 .....please explain



Math Expert
Joined: 02 Sep 2009
Posts: 49303

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
17 Oct 2013, 04:56



Manager
Joined: 11 Sep 2013
Posts: 162
Concentration: Finance, Finance

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
22 Oct 2013, 15:00
there are many hard data sufficiency questions? To get over 700 in GMAT at least how many hard data sufficiency questions do we have to answer? I have a lot of problems with hard and tricky DS questions. I always go close to the answer but finally make mistake in hard DS by not noticing one or two things. Can anyone help me please?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8288
Location: Pune, India

Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1
[#permalink]
Show Tags
22 Oct 2013, 21:31
Raihanuddin wrote: there are many hard data sufficiency questions? To get over 700 in GMAT at least how many hard data sufficiency questions do we have to answer? I have a lot of problems with hard and tricky DS questions. I always go close to the answer but finally make mistake in hard DS by not noticing one or two things. Can anyone help me please? Half or more than half of the Quant section consists of DS questions. To get over 700, you need to be able to handle 700 level questions of DS as well. DS questions have a lot of traps and it pays to be aware of them. You can check out the Veritas DS book. It has excellent discussions on DS traps, common error areas and strategies. It's a must have if you are facing problems in DS but are relatively comfortable in PS because then you have DS format issues and need a book which addresses those specifically.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!




Re: Is A positive? (1) x^2  2x + A is positive for all x (2) Ax^2 + 1 &nbs
[#permalink]
22 Oct 2013, 21:31



Go to page
1 2
Next
[ 32 posts ]



