Data Sufficiency

Question : Is k.k + k - 2 > 0 ?

1) k < 1

2) k > -1

The usual 5 answers .

Here is what I did:

k.k + k - 2 > 0 ?

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

1) isnt enough because k-1 will always be negative but k+ 2 can be negative , but it can be positive os we don`t know whether k.k + k - 2 > 0 is >0 or < 0

2) since k > - 1 k + 2 and k - 1 will both always be positive so k.k + k - 2 > 0 .So I thought 2 alone is enough,

However,the correct answer is given as C - both statements are needed.

Any thoughts ?

sapuna wrote:Question : Is k.k + k - 2 > 0 ?

1) k < 1

2) k > -1

Question : Is k^2 + k - 2 > 0 ?

Question : Is (k+2)(k-1) > 0 ?

Question Rephrased : Is k > 1 ? or Is k < -2?
Question Rephrased : Is -2 < k < 1 ?

Statement 1) k < 1
It may be in range (e.g. k = 0) or may NOT be in the range (e.g. k = -10) asked in the Rephrased Question, therefore

INSUFFICIENT

Statement 2) k > -1
It may be in range (e.g. k = 0) or may NOT be in the range (e.g. k = 10) asked in the Rephrased Question, therefore

INSUFFICIENT

Combining the two statements
k > -1 and k < 1
i.e. -1<k<1
It DEFINITELY falls in range asked in the Rephrased Question, therefore
SUFFICIENT

Answer: Option C

sapuna wrote:Question :

Here is what I did:

k.k + k - 2 > 0 ?

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

1) isnt enough because k-1 will always be negative but k+ 2 can be negative , but it can be positive os we don`t know whether k.k + k - 2 > 0 is >0 or < 0

2) since k > - 1 k + 2 and k - 1 will both always be positive so k.k + k - 2 > 0 .So I thought 2 alone is enough,

However,the correct answer is given as C - both statements are needed.

Any thoughts ?

The highlighted (Red) part shows your mistake.

If k>-1
@k = -0.5
k + 2 = 1.5 Positive
But k - 1 = -1.5 Negative

and
@k = 10 [which is greater than -1]
k + 2 = 12 Positive
k - 1 = 9 Positive

INCONSISTENCY in responses therefore INSUFFICIENT

Blahh , too much GMAT lately to be honest. Easy question , silly mistake on my part. In statement 2) I was thinking K > 1 in which case the product of the two would always be positive. However, the statement said that K > -1 , in which case the numbers between - 1 and 1 would be a problem. Thank you again. Sorry for wasting your time a bit

sapuna wrote:Blahh , too much GMAT lately to be honest. Easy question , silly mistake on my part. In statement 2) I was thinking K > 1 in which case the product of the two would always be positive. However, the statement said that K > -1 , in which case the numbers between - 1 and 1 would be a problem. Thank you again. Sorry for wasting your time a bit

A rejuvenating Break intermittently is always called for when you prepare for any competitive examination!!!