It is currently 22 Jun 2017, 21:07

### 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

# m13/q23....wrong ans

Author Message
Verbal Forum Moderator
Joined: 02 Aug 2009
Posts: 4558

### Show Tags

03 Jan 2010, 09:27
Is A positive?

i)x^2-2x+A is positive for all x
ii)Ax^2+1 is positive for all x
reason given < Statement (1) by itself is sufficient. x^2-2x+A = (x-1)^2+(A-1) . For this expression to be always positive (A-1) has to be more than 0.so A has to be more than 1>
A can be any -ive int till (x-1)^2 is greater than (A-1)... ex x=3... 4+A-1>0.. or A>-3
ans shud be E...pl confirm
i think where we have gone wrong is taking + in(x-1)^2+(A-1) as *....
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Math Expert
Joined: 02 Sep 2009
Posts: 39589

### Show Tags

03 Jan 2010, 18:13
chetan2u wrote:
Is A positive?

i)x^2-2x+A is positive for all x
ii)Ax^2+1 is positive for all x
reason given < Statement (1) by itself is sufficient. x^2-2x+A = (x-1)^2+(A-1) . For this expression to be always positive (A-1) has to be more than 0.so A has to be more than 1>
A can be any -ive int till (x-1)^2 is greater than (A-1)... ex x=3... 4+A-1>0.. or A>-3
ans shud be E...pl confirm
i think where we have gone wrong is taking + in(x-1)^2+(A-1) as *....

Step by step:

Question: is $$A>0$$?

(1) $$x^2-2x+A$$ is positive for all $$x$$:

$$f(x)=x^2-2x+A$$ is a function of of upward parabola. We are told that it's positive for all $$x$$ --> $$f(x)=x^2-2x+A>0$$, which means that this function is "above" X-axis OR in other words parabola has no intersections with X-axis OR equation $$x^2-2x+A=0$$ has no real roots.

Quadratic equation to has no real roots discriminant must be negative --> $$D=2^2-4A=4-4A<0$$ --> $$1-A<0$$ --> $$A>1$$.

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.

So I think the answer (A) is correct.
_________________
Verbal Forum Moderator
Joined: 02 Aug 2009
Posts: 4558

### Show Tags

04 Jan 2010, 04:43
hi .....
i do understand that as an eq of parabola c would be y-intercept and parabola being limited to i and ii quad , c would be always +ive...... but why cant we prove it taking it as a normal eq (as it wud seem to any layperson)... is there any way to prove it
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Re: m13/q23....wrong ans   [#permalink] 04 Jan 2010, 04:43
Similar topics Replies Last post
Similar
Topics:
1 m17 #33 Incorrect Ans? 6 17 Feb 2012, 20:45
18 M02 02 : Not convinced with method used to explaing the ans 16 20 Nov 2013, 11:36
Display posts from previous: Sort by

# m13/q23....wrong ans

Moderator: Bunuel

 Powered by phpBB © phpBB Group and phpBB SEO 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®.