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:

(1) when x is negative, A must be positive; when x is positive, A can either be positive or negative. Since the value of A has to result in a positive outcome for all values of x, A is positive

(1) when x is negative, A must be positive; when x is positive, A can either be positive or negative. Since the value of A has to result in a positive outcome for all values of x, A is positive

Statement 1 is sufficient

(2) A can be either positive or zero.

statement 2 is insufficient

Answer:A

Take x =4 and A = 2 the equation is satisfied.
Take x =4 and A = -1 the equation is satisfied.
So A can be +ve or -ve. So stmt1 is INSUFF

(1) when x is negative, A must be positive; when x is positive, A can either be positive or negative. Since the value of A has to result in a positive outcome for all values of x, A is positive

Statement 1 is sufficient

(2) A can be either positive or zero.

statement 2 is insufficient

Answer:A

Take x =4 and A = 2 the equation is satisfied. Take x =4 and A = -1 the equation is satisfied. So A can be +ve or -ve. So stmt1 is INSUFF

vshaunak
------------
The value of A must span all values of X .. ALL values .. small negative fractions, large positive integers .. etc

try x = -0.5 --> A must be positive in order for the condition to apply.
The value of A that results in a positive value of the equation for ALL values of X .. [ all and any value of X ] is a positive A

(D) for me ..... Excellent question that goes deep in the concept of curves

A > 0 ?

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) <=> 4 - 4*A*1 < 0 <=> 4*A > 4 <=> A > 1 > 0

SUFF.

From 2 A*x^2 + 1 > 0

Meaning that : b^2 - 4*a*c < 0 (this is the descriminat of a*x^2 + b*x + c) and A must be positive to create a valley shape for the curve A*x^2 + 1.

SUFF.

Fig, there is a mistake in your solution
b^2 - 4*a*c > 0 for the real roots.
4-4A > 0
A < 1
Hence this holds true for +ve as well as for -ve values of A.
Stmt1 is NOT suff.

The case A=0 for the second case is possible... My mistake... the equation of a*x^2+b*x+c was an assertion without having checked the special case A=0 that works perfectly (0*x^2 + 1 = 1 > 0).

(D) for me ..... Excellent question that goes deep in the concept of curves

A > 0 ?

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) <=> 4 - 4*A*1 < 0 <=> 4*A > 4 <=> A > 1 > 0

SUFF.

From 2 A*x^2 + 1 > 0

Meaning that : b^2 - 4*a*c < 0 (this is the descriminat of a*x^2 + b*x + c) and A must be positive to create a valley shape for the curve A*x^2 + 1.

SUFF.

Fig, there is a mistake in your solution b^2 - 4*a*c > 0 for the real roots. 4-4A > 0 A < 1 Hence this holds true for +ve as well as for -ve values of A. Stmt1 is NOT suff.

Yes... agree .... I should not come to reply so late after an exhausting day :p.... Completly wrong here....

vshaunak ------------ The value of A must span all values of X .. ALL values .. small negative fractions, large positive integers .. etc

try x = -0.5 --> A must be positive in order for the condition to apply. The value of A that results in a positive value of the equation for ALL values of X .. [ all and any value of X ] is a positive A

(D) for me ..... Excellent question that goes deep in the concept of curves

A > 0 ?

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) <=> 4 - 4*A*1 < 0 <=> 4*A > 4 <=> A > 1 > 0

SUFF.

From 2 A*x^2 + 1 > 0

Meaning that : b^2 - 4*a*c < 0 (this is the descriminat of a*x^2 + b*x + c) and A must be positive to create a valley shape for the curve A*x^2 + 1.

SUFF.

Fig, there is a mistake in your solution b^2 - 4*a*c > 0 for the real roots. 4-4A > 0 A < 1 Hence this holds true for +ve as well as for -ve values of A. Stmt1 is NOT suff.

Yes... agree .... I should not come to reply so late after an exhausting day :p.... Completly wrong here....

It's so (E)... Agree .... Excellent catch ! :D

No... After 1 shower to wake me up, I have read again your sign at start.... I was thinking I had flipped one... but no

Actually, I really wanted to say b^2 - 4 * a * c < 0.... to force the curve to be always of the sign of a... Here a=1 and so always positive.

Sorry guys.... the answer must be (A)

Last edited by Fig on 09 Jun 2007, 14:31, edited 1 time in total.

A side question Fig: really why do you still participate in GMAT topics and posts in the forum ? you're already waay beyond GMAT .. You're mastered it.

Mishari, I think the answer to this question is.... (E) non of the statments are sufficient

More seriously, I feel it as a win win situation. By my side, I have time and the will to keep me uptodate and studying. By the community side, I try to clarify the points that I can and if it means some guys learn something from it to kill the GMAT.... that's an excellent plus !

Also, it's a question of personnality & appreciation. I like Math for a while and I like to give back what I recieved ... The GMATClub was an amazing source of information and learnings during the whole application process, a process very demanding in energy and time. It was so not so much possible for me to compensate in a certain way what I recieved.... It's a kind of pay back now with high interest (rate;)) and entertainements ..... I must admit also that I'm a kind of handy guy, but do not repeat it

That said, I will probably be much less accessible after December 2007. It will be the time for me to move on into the School.

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...