Bunuel wrote:

Is k^2 + k – 2 > 0?

(1) k < 1

(2) k > –1

Hi...

Let's simplify the equation

\(k^2+k-2>0.........k^2+2k-k-2>0......k(k+2)-1(k+2)>0.....(k+2)(k-1)>0\)..

So both k+2 and k-1 should be of same SIGN..

So a)k between -2 and 1 will give us and NO

b) K<-2 and k>1 will give us and YES

Let's see the statements..

1) k<1...

It will give us falling in both above ranges, so ans can be yes or no

Insufficient

2) k>-1

Same as above

K=0 will give us no

K=5 will give YES

Insufficient

Combined

-1<k<1

This range falls within (a) above

ANS is always NO

Sufficient

C

I don't understand this. Doesn't the formula simplify to the following

4) k > 2 and k > 1 => So K must be greater than 1 to be more than 0