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
simple data sufficiency...
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Source: Beat The GMAT — Data Sufficiency |
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VerbalAttack
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Hi vaivish, what does k <1> -1 stands for?vaivish wrote:Is k² + k - 2 > 0
(1) k <1> -1
is it k not equals -1?
also pls provide other answer choices..
cheers
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egybs
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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.
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.
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egybs
- Master | Next Rank: 500 Posts
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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.
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
