C) The key to this problem is to factor k² + k - 2 into (k + 2) (k - 1). The product of the two expressions is positive if and only if both expressions have the same sign. When (1) holds, then k - 1 is negative, but k + 2 can be positive or negative, so (1) alone is not sufficient. When (2) holds, then k + 2 is positive, but k - 1 can be positive or negative, so (2) alone is not sufficient. However, if both (1) and (2) are true, then k is between -1 and 1 and so k + 2 is positive and k - 1 is negative, which means (k + 2) (k - 1) is negative. This is sufficient to answer the question.

I am not convinced with the ans as it is not mentioned that K has be be an integer...This ans only holds in case of integer K which we have to assume.....Please help

can you give us the full question?

Is k² + k - 2 > 0

(1) k <1> -1

vaivish wrote:Is k² + k - 2 > 0

(1) k <1> -1

Hi vaivish, what does k <1> -1 stands for?

is it k not equals -1?

also pls provide other answer choices..

cheers

Is k² + k - 2 > 0

(1) k <1> -1

Its a data sufficiency question with the already posted ans....

Are you trying to mess with us?

Data sufficiency questions have 2 pieces of data, (1) and (2)... You only gave us (1). We need the other to come up with an answer.

Also, as far as I know, "k <1> -1" is not standard notation... If you meant K does not equal -1, then please let us know.

Regardless... Just by looking at the question, we know the following:

Is k² + k - 2 > 0

(k+2)(k-1) > 0

Which means that k cannot be equal to -2 or 1... and must be bigger than 1 or less than -2 since both sides need to be either positive or negative.

So the question really is, "is -2>k OR k>1 true?"

So we're looking for the choices that can answer this question.

Is k² + k - 2 > 0
K > -1
K < 1

OK.. so from my previous post, i explained that the question is actually asking us if -2>k OR k>1 is true?

based on the answers you just provided:
(1) k> -1 - this doesn't tell us enough to decide if the inequality is true or not... if k is 0 the inequality is false, but k could also be 100 which would make it true.

(2) k < 1 - this doesn't tell us enough either. K could be -3 which would make the inequality true, but it could also be zero, which would make it false.

Together, they tell us that k is between -1 and 1, not inclusive. From before, we now know enough to determine that the inequality is false.

So the answer is that both, together, are sufficient.

vaivish wrote:Is k² + k - 2 > 0
K > -1
K < 1

Thread moved to the DS section.