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# s05#2

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Intern
Joined: 24 Mar 2012
Posts: 10

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10 May 2012, 03:10
Is A Positive ?

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

Official Explanation -
============================
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. A has to be more than 1.

Statement (2) by itself is insufficient. Ax^2+1 is positive for all even if A is 0.

==========================

x^2 -2x + A > 0 for all x
=> (x-1)^2 + (A-1) > 0 for all x

now, lets say if x-1=root5, (x-1)^2 = 5,

A can be 3, hence, the expression becomes 5 + 2 = 7 > 0 ,
Is A positive, answer to question is YES
A can be -3, hence, the expression becomes 5 - 4 = 1 > 0 ,
Is A positive, answer to question is NO

Not sure if I miss something.

Kudos [?]: [0], given: 1

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129029 [1], given: 12187

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10 May 2012, 03:15
1
KUDOS
Expert's post
mitrahere wrote:
Is A Positive ?

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

Official Explanation -
============================
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. A has to be more than 1.

Statement (2) by itself is insufficient. Ax^2+1 is positive for all even if A is 0.

==========================

x^2 -2x + A > 0 for all x
=> (x-1)^2 + (A-1) > 0 for all x

now, lets say if x-1=root5, (x-1)^2 = 5,

A can be 3, hence, the expression becomes 5 + 2 = 7 > 0 ,
Is A positive, answer to question is YES
A can be -3, hence, the expression becomes 5 - 4 = 1 > 0 ,
Is A positive, answer to question is NO

Not sure if I miss something.

Welcome to GMAT Club. This question is discussed here: is-a-positive-x-2-2x-a-is-positive-for-all-x-ax-2-1-is-97302.html

_________________

Kudos [?]: 129029 [1], given: 12187

Intern
Joined: 24 Mar 2012
Posts: 10

Kudos [?]: [0], given: 1

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10 May 2012, 03:29
Thanks much Bunuel. That explains my query.

Kudos [?]: [0], given: 1

Re: s05#2   [#permalink] 10 May 2012, 03:29
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# s05#2

Moderator: Bunuel

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