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 350,000 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:

If x=1/2, then x^2-2x+A = -3/4 + A. So A -> positive if x^2-2x+A is positive.
If x=5, then x^2-2x+A = 15+A. So A -> positive or A is negative but bigger than -15. However, since we're saying that it must be all x, A must be positive otherwise fractional x wouldn't work. Sufficient.

St2:
A*x^2 + 1 is positive for all x

If x=1/2, then A*x^2 + 1 = A/4 + 1. A can be negative or positive and A*x^2 + 1 will be positive.

If x=2, then A*x^2 + 1 = 4a + 1. A has to be positive if A*x^2 + 1 is positive. Since we want A*x^2 + 1 to be positive for all x, then A has to be positive if not integer values of x won't work. Sufficient.

If x=1/2, then x^2-2x+A = -3/4 + A. So A -> positive if x^2-2x+A is positive. If x=5, then x^2-2x+A = 15+A. So A -> positive or A is negative but bigger than -15. However, since we're saying that it must be all x, A must be positive otherwise fractional x wouldn't work. Sufficient.

St2: A*x^2 + 1 is positive for all x

If x=1/2, then A*x^2 + 1 = A/4 + 1. A can be negative or positive and A*x^2 + 1 will be positive.

If x=2, then A*x^2 + 1 = 4a + 1. A has to be positive if A*x^2 + 1 is positive. Since we want A*x^2 + 1 to be positive for all x, then A has to be positive if not integer values of x won't work. Sufficient.

Ans D

I disagree with D.

From stmt 1 we know A > 2x. This doesnt mean that A is positive or negative.
From Stmt 2 we know that A > -1/x^2. So no clue here too

Re: DS: Is A positive? [#permalink]
18 Sep 2007, 12:55

GK_Gmat wrote:

Is A positive?

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

Pls. explain. Thanks.

i think it is E

1) A could be positive or negative
ex. x = 4, A = -5 -> 4^2 - 2(4) - 5 = 3
stmt still true

ex. x = 4, A = 5 -> 4^2 - 2(4) + 5 = 13
stmt still true

2) A could be either again since does not specify whether int or not
x^2 is always positive but A can be neg (if the product for A* x^2 is -1/2 for instance.. stmt still holds true) or A can positive and yield a positive answer

Re: DS: Is A positive? [#permalink]
18 Sep 2007, 14:29

GK_Gmat wrote:

Is A positive?

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

Pls. explain. Thanks.

1: x^2 - 2x +A > 0

refrese the inequality as : x^2 - 2x + 1 + A -1 > 0
so it is reduced to (x - 1)^2 + A – 1 > 0.
now (x -1)^2 can be 0 or grater than 0. if it is 0, A - 1 has to be +ve and to be so, A has to be grater than 1. so suff.

2: A*x^2 + 1 is positive for all x.

it is clearly insufficient because x^2 is 0, A could be +ve or -ve and the expression still is +ve..

Re: DS: Is A positive? [#permalink]
18 Sep 2007, 14:51

Fistail wrote:

GK_Gmat wrote:

Is A positive?

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

Pls. explain. Thanks.

1: x^2 - 2x +A > 0

refrese the inequality as : x^2 - 2x + 1 + A -1 > 0 so it is reduced to (x - 1)^2 + A – 1 > 0. now (x -1)^2 can be 0 or grater than 0. if it is 0, A - 1 has to be +ve and to be so, A has to be grater than 1. so suff.

2: A*x^2 + 1 is positive for all x.

it is clearly insufficient because x^2 is 0, A could be +ve or -ve and the expression still is +ve..

so A works here.

Indeed a good approach Fistail.

But how about putting the value of x = -1 and obtaining the possible values of A as I mentioned in my above earlier post?

Re: DS: Is A positive? [#permalink]
18 Sep 2007, 15:05

b14kumar wrote:

Fistail wrote:

GK_Gmat wrote:

Is A positive?

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

Pls. explain. Thanks.

1: x^2 - 2x +A > 0

refrese the inequality as : x^2 - 2x + 1 + A -1 > 0 so it is reduced to (x - 1)^2 + A – 1 > 0. now (x -1)^2 can be 0 or grater than 0. if it is 0, A - 1 has to be +ve and to be so, A has to be grater than 1. so suff.

2: A*x^2 + 1 is positive for all x.

it is clearly insufficient because x^2 is 0, A could be +ve or -ve and the expression still is +ve..

so A works here.

Indeed a good approach Fistail.

But how about putting the value of x = -1 and obtaining the possible values of A as I mentioned in my above earlier post?

Writing again:

ST1: x^2 - 2x +A is positive for all x

Let's say x = -1

Then, 1 + 2 + A > 0 => 3 + A > 0 => A > (-3)

So A may be -2 , -1 , 0 or > 0

Hence A may be positive or negative.

- Brajesh

I again looked at your approach.

As per you:

refrese the inequality as : x^2 - 2x + 1 + A -1 > 0 so it is reduced to (x - 1)^2 + A – 1 > 0. now (x -1)^2 can be 0 or grater than 0. if it is 0, A - 1 has to be +ve and to be so, A has to be grater than 1. so suff. Why are you assuming only the case when (x-1)^2 is equal to 0?

Well, (x -1)^2 will always be >= 0 but it does not mean that "A – 1" has to be positive for all the cases.
Imagine, (x -1)^2 is equal to 4 (by taking x = 3 ) , in this case, (A-1) can be (-3) i.e A can be (-2) and still the whole inequality will be intact.

Re: DS: Is A positive? [#permalink]
18 Sep 2007, 22:00

b14kumar wrote:

b14kumar wrote:

Fistail wrote:

GK_Gmat wrote:

Is A positive?

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

Pls. explain. Thanks.

1: x^2 - 2x +A > 0

refrese the inequality as : x^2 - 2x + 1 + A -1 > 0 so it is reduced to (x - 1)^2 + A – 1 > 0. now (x -1)^2 can be 0 or grater than 0. if it is 0, A - 1 has to be +ve and to be so, A has to be grater than 1. so suff.

2: A*x^2 + 1 is positive for all x.

it is clearly insufficient because x^2 is 0, A could be +ve or -ve and the expression still is +ve..

so A works here.

Indeed a good approach Fistail.

But how about putting the value of x = -1 and obtaining the possible values of A as I mentioned in my above earlier post?

Writing again:

ST1: x^2 - 2x +A is positive for all x

Let's say x = -1

Then, 1 + 2 + A > 0 => 3 + A > 0 => A > (-3)

So A may be -2 , -1 , 0 or > 0

Hence A may be positive or negative.

- Brajesh

I again looked at your approach.

As per you:

refrese the inequality as : x^2 - 2x + 1 + A -1 > 0 so it is reduced to (x - 1)^2 + A – 1 > 0. now (x -1)^2 can be 0 or grater than 0. if it is 0, A - 1 has to be +ve and to be so, A has to be grater than 1. so suff. Why are you assuming only the case when (x-1)^2 is equal to 0?

Well, (x -1)^2 will always be >= 0 but it does not mean that "A – 1" has to be positive for all the cases. Imagine, (x -1)^2 is equal to 4 (by taking x = 3 ) , in this case, (A-1) can be (-3) i.e A can be (-2) and still the whole inequality will be intact.

Please let me know your opinion.

- Brajesh

The OA is A. But it doesn't make sense. I'm having the same problem understanding the solution as Brijesh (Above). Any thoughts?

The catch in this question is that A is CONSTATNT not a variable. So for all x, A will have the same value.

Now read it as - Find the value of A (+/-) for which x^2 - 2x + A > 0 is true for all x.
Paraphrase this (x-1)^2 + A-1 > 0
The minimum value of (x-1)^2 is zero. So A > 1.
So A> 1 satisfies the expression for all x.
Hence SUFF.

Stmt2: Ax^2 + 1 > 0
If we take A -ve, the above expression will be true for some cases and false for some cases depending on value of x. To make this true for all x, A should be +ve or zero.
So INSUFF.

My answer is 'A'

Last edited by vshaunak@gmail.com on 21 Sep 2007, 03:02, edited 1 time in total.

The catch in this question is that A is CONSTATNT not a variable. So for all x, A will have the same value.

Now read it as - Find the value of A (+/-) for which x^2 - 2x + A > 0 is true for all x. Paraphrase this (x-1)^2 + A-1 > 0 The minimum value of (x-1)^2 is zero. So A > 1. So A> 1 satisfies the expression for all x. Hence SUFF.

Stmt2: Ax^2 + 1 > 0 If we take A -ve, the above expression will be true for some cases and false for some cases depending on value of x. To make this true for all x, A should be +ve. So SUFF.

My answer is 'D'

I think OA is correct as A .
For Stmtn 1 - same as marked as blue .

For Stmtn 2 - you can never determine whether A is +ve or -ve

Ax^2 + 1 = 0.5 => A = -ve
Ax^2 +1 = 2 => A = +ve
So stmtn is not suff .

This week went in reviewing all the topics that I have covered in my previous study session. I reviewed all the notes that I have made and started reviewing the Quant...

I was checking my phone all day. I wasn’t sure when I would receive the admission decision from Tepper. I received an acceptance from Goizueta in the early morning...

I started running as a cross country team member since highshcool and what’s really awesome about running is that...you never get bored of it! I participated in...