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# m13/q23....wrong ans

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Math Forum Moderator
Joined: 02 Aug 2009
Posts: 4986

Kudos [?]: 5498 [0], given: 112

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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

Kudos [?]: 5498 [0], given: 112

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129078 [0], given: 12194

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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.
_________________

Kudos [?]: 129078 [0], given: 12194

Math Forum Moderator
Joined: 02 Aug 2009
Posts: 4986

Kudos [?]: 5498 [0], given: 112

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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

Kudos [?]: 5498 [0], given: 112

Re: m13/q23....wrong ans   [#permalink] 04 Jan 2010, 04:43
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# m13/q23....wrong ans

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