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(1) \(a^2+b^2=1\) --> is \(1>-a\) or is \(a>-1\), not sufficient. For example if \(a=1\) and \(b=0\) then the answer will be YES but if \(a=-1\) and \(b=0\) then the answer will be NO.

(2) \(a>0\) --> so \(a^2+a+b^2=(positive)+(positive)+(non-negative)\) which is clearly positive, so \(a^2+a+b^2>0\). Sufficient.

Is a^2 + a > -b^2? [#permalink]
23 Nov 2014, 07:45

Creeper300 wrote:

Is a^2 + a > -b^2?

(1) a^2 + b^2 = 1 (2) a > 0

did it in the following way:

question becomes: is a^2 + b^2 + a > 0, as the minimum value of a^2 + b^2 is 0, the question is is a> 0?

from statement 1: a^2 + b^2 = 1, which reduces to a> -1, when a = b= 0 then a = 0 and not greater than 0, so NSF statement 2 directly answers the question, sufficient

Re: Is a^2 + a > -b^2? [#permalink]
26 Nov 2014, 18:16

Bunuel wrote:

Creeper300 wrote:

a^2+a > -b^2?

1. a^2+ b^2=1 2. a>0

Is \(a^2+b^2>-a\)? or is \(a^2+a+b^2>0\)

(1) \(a^2+b^2=1\) --> is \(1>-a\) or is \(a>-1\), not sufficient. For example if \(a=1\) and \(b=0\) then the answer will be YES but if \(a=-1\) and \(b=0\) then the answer will be NO.

(2) \(a>0\) --> so \(a^2+a+b^2=(positive)+(positive)+(non-negative)\) which is clearly positive, so \(a^2+a+b^2>0\). Sufficient.

Answer: B.

Hi Bunnel ,

Shouldnt this be D , since statement (1) gives a>-1 ,so a cannot be negative , and both a & b are not zero (a^2 + b^=1).

Re: Is a^2 + a > -b^2? [#permalink]
27 Nov 2014, 02:14

Expert's post

mattapattu wrote:

Bunuel wrote:

Creeper300 wrote:

a^2+a > -b^2?

1. a^2+ b^2=1 2. a>0

Is \(a^2+b^2>-a\)? or is \(a^2+a+b^2>0\)

(1) \(a^2+b^2=1\) --> is \(1>-a\) or ", not sufficient. For example if \(a=1\) and \(b=0\) then the answer will be YES but if \(a=-1\) and \(b=0\) then the answer will be NO.

(2) \(a>0\) --> so \(a^2+a+b^2=(positive)+(positive)+(non-negative)\) which is clearly positive, so \(a^2+a+b^2>0\). Sufficient.

Answer: B.

Hi Bunnel ,

Shouldnt this be D , since statement (1) gives a>-1 ,so a cannot be negative , and both a & b are not zero (a^2 + b^=1).

You missed a point there.

(1) says that \(a^2+b^2=1\). If we substitute this into the question (is \(a^2+a+b^2>0\)?), the question becomes "is \(a>-1\)?". As shown in the solution it can be more than -1 (a=1 and b=0) as well as equal to -1 (a=-1 and b=0). So, we cannot answer the question with a definite YES or NO. Thus the statement is not sufficient.

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