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.
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club
Registration gives you:
Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.
Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more
Books/Downloads
Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
How can it be A?
x^2-2*x + A>0
A>2*x-x^2
assume x=1
A>2-1
A>1 --> A is positiv
assume x=3
A>6-9
A>-3
A might be -2, -1, 0 1 and so on...
So (1) is insuff
ok..Now I will try to get A
x^2-2*x +A is a parabola
x^2-2*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;A-1)
y-coord of min point of this parabola = A-1
y-coord must be > 0
A-1>0
A>1
A - positive
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.
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 , 1-2+A>0 A-1>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, 19:04, edited 1 time in total.
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.
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
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.
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
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)
You know what’s worse than getting a ding at one of your dreams schools . Yes its getting that horrid wait-listed email . This limbo is frustrating as hell . Somewhere...
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Wow! MBA life is hectic indeed. Time flies by. It is hard to keep track of the time. Last week was high intense training Yeah, Finance, Accounting, Marketing, Economics...