It is currently 23 Mar 2018, 00:22

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
Current Student
Joined: 11 May 2008
Posts: 552
Is A positive? 1. x^2 - 2x + A is positive for all x 2. Ax^2 [#permalink]

### Show Tags

01 Sep 2008, 04:31
1
This post was
BOOKMARKED
Is $$A$$ positive?

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

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Senior Manager
Joined: 09 Oct 2007
Posts: 459

### Show Tags

01 Sep 2008, 07:32
I'd go for A.

S1) A = +1. SUFF.
S2) A(x^2)+1 = POS ==> A(x^2) = POS-1, thus A(x^2) could equal a positive number or zero. A could be any positive number or zero, which is not positive. INSUFF.
Current Student
Joined: 11 May 2008
Posts: 552

### Show Tags

01 Sep 2008, 10:48
how do u say 1 is suff??
Manager
Joined: 12 Feb 2008
Posts: 176

### Show Tags

01 Sep 2008, 11:41
asdert wrote:
I'd go for A.

S1) A = +1. SUFF.
S2) A(x^2)+1 = POS ==> A(x^2) = POS-1, thus A(x^2) could equal a positive number or zero. A could be any positive number or zero, which is not positive. INSUFF.

lets say X=5, and A=10
then 1) 25-10+10>0
but if x=5, and A=-10
then 25-10-10>10
same is true for A=0
so A is Insufficient

2) A can be either 0, or A>0, also insufficient
IMO both are also insufficient.

what is the OA?
Senior Manager
Joined: 09 Oct 2007
Posts: 459

### Show Tags

01 Sep 2008, 12:02
I solved by undisguising the quadratic, but I may be wrong:
$$(x-1)(x-1) = x^2-2x+1,$$ thus A = 1 = SUFF.

I hate picking random numbers in problems like this because they don't always work:
$$x^2 - 2x + A$$ is positive for all $$x$$

If A = -10, then result must be positive for all X. So what if X is -2?
$$(-2)^2 - (-4) + (-10) =$$ POSITIVE
$$4 + 4 - 10 =$$NEGATIVE
At least that's what I think.
SVP
Joined: 07 Nov 2007
Posts: 1759
Location: New York

### Show Tags

01 Sep 2008, 12:33
arjtryarjtry wrote:
Is $$A$$ positive?

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

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

A> -x^2+2x -- true for all values of x.

please note that here A is constant and x is variable..

Find out the possible values of "-x^2+2x"

"-x^2+2x" +ve when X=1 --(1)
"-x^2+2x" -ve when X=3 --(2)

from (1) it is clear that A>+ve so it is positive.
from (2) it is clear that A>-ve so it can positive or negative.

It has to satisfy both equations 1 and 2
A must be positive.

Suffcieint

2)
Ax^2 + 1>0

A> -1/x^2
--> Tells that for all values X A> -ve number.

So A can be +ve or -ve

Insuffcient

_________________

Smiling wins more friends than frowning

VP
Joined: 05 Jul 2008
Posts: 1369

### Show Tags

01 Sep 2008, 13:04
x2suresh wrote:
arjtryarjtry wrote:
1) x^2 - 2x + A >0

A> -x^2+2x -- true for all values of x.

please note that here A is constant and x is variable..

Find out the possible values of "-x^2+2x"

"-x^2+2x" +ve when X=1 --(1)
"-x^2+2x" -ve when X=3 --(2)

from (1) it is clear that A>+ve so it is positive.
from (2) it is clear that A>-ve so it can positive or negative.

It has to satisfy both equations 1 and 2
A must be positive.

Suffcieint

.

Why does it have to satisfy both equations?

x^2 -2x + A > 0 for all X

x=-1 range of x = { -2, -1 ... infinity} both +ve and -ve

x=-2 range of x = {-7, -6 .. infinity } both -ve and +ve

x= 0 A >0

x=1 A >1

X=2 A>0

X=3 A >-3 again both +ve and -ve

May be is not sufficient

My pick is E
Manager
Joined: 14 Jun 2008
Posts: 162

### Show Tags

02 Sep 2008, 04:31
x2suresh wrote:
arjtryarjtry wrote:
Is $$A$$ positive?

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

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

A> -x^2+2x -- true for all values of x.

please note that here A is constant and x is variable..

Find out the possible values of "-x^2+2x"

"-x^2+2x" +ve when X=1 --(1)
"-x^2+2x" -ve when X=3 --(2)

from (1) it is clear that A>+ve so it is positive.
from (2) it is clear that A>-ve so it can positive or negative.

It has to satisfy both equations 1 and 2
A must be positive.

Suffcieint

2)
Ax^2 + 1>0

A> -1/x^2
--> Tells that for all values X A> -ve number.

So A can be +ve or -ve
Insuffcient

i dont think A can be negative
because as soon as A becomes the negative, the parabola will be inverted, and you cannot gurantee that for all values of x, $$Ax^2 + 1$$ is positive for all $$x$$[/quote]

but the equation sez other wise.
i am confused !!!
SVP
Joined: 17 Jun 2008
Posts: 1502

### Show Tags

02 Sep 2008, 05:08
I approached the problem as below.

Stmt 1: x^2 - 2x + A is positive for all x. That means this expression should be positive even for x = 0. With x = 0, the expression changes to A. And, if the expression is positive, A must be positive. Hence, sufficient.

Stmt2: Not sufficient. For a positive value as well as negative value of x, the expression can be positive.
SVP
Joined: 07 Nov 2007
Posts: 1759
Location: New York

### Show Tags

02 Sep 2008, 06:28
sset009 wrote:
x2suresh wrote:
arjtryarjtry wrote:
Is $$A$$ positive?

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

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

A> -x^2+2x -- true for all values of x.

please note that here A is constant and x is variable..

Find out the possible values of "-x^2+2x"

"-x^2+2x" +ve when X=1 --(1)
"-x^2+2x" -ve when X=3 --(2)

from (1) it is clear that A>+ve so it is positive.
from (2) it is clear that A>-ve so it can positive or negative.

It has to satisfy both equations 1 and 2
A must be positive.

Suffcieint

2)
Ax^2 + 1>0

A> -1/x^2
--> Tells that for all values X A> -ve number.

So A can be +ve or -ve
Insuffcient

i dont think A can be negative
because as soon as A becomes the negative, the parabola will be inverted, and you cannot gurantee that for all values of x, $$Ax^2 + 1$$ is positive for all $$x$$

but the equation sez other wise.
i am confused !!! [/quote]

Ax^2 + 1>0

A> -1/x^2

say x=1 A>-1 means A can be -1/2 or zero or Any postive value.
_________________

Smiling wins more friends than frowning

Senior Manager
Joined: 31 Jul 2008
Posts: 280

### Show Tags

02 Sep 2008, 11:46
E for me :

1 is not sufficient ;

x^2-2x + A > 0

here imagine that the value of x is +5 , then the equation becomes 25-10 +A ; now if A is -1/+1 OR -2/+2 etc doesnt make any diff. as the answer will always be
+ve ; same is the case if you take x=-5 .

2 is obv not sufficient as many people have agreed

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: A+VE   [#permalink] 02 Sep 2008, 11:46
Display posts from previous: Sort by

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

Moderator: chetan2u

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne 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®.