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(1) k is an integer greater than zero. (2) k divided by 2 is an integer.

Kudos for a correct solution.

Question : Is k^2 + k – 2 > 0? i.e. Question : Is k^2 + 2k - k – 2 > 0? i.e. Question : Is (k + 2) (k - 1) > 0?

i.e. Question : Is k < -2 OR k > 1?

Statement 1: k is an integer greater than zero. @k=1, (k + 2) (k - 1) is NOT greater than 0 @k=2, (k + 2) (k - 1) is greater than 0 NOT SUFFICIENT

Statement 2: k divided by 2 is an integer. i.e. k is an Even Number so k can be 0 or 2 or 4 etc. hence, NOT SUFFICIENT

Combining the two statements: i.e. k is an Even Number greater than zero so k can be 2 or 4 or 6 etc and for all values of k now (k + 2) (k - 1) is greater than 0 SUFFICIENT

Answer: Option C
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(1) k is an integer greater than zero. (2) k divided by 2 is an integer.

Kudos for a correct solution.

Is k^2 + k – 2 > 0? -----> (k-1)(k+2) ---> is k>1 or k<-2

Per statement 1, k>0 . Now this value of k can be 1 (so k>1 is not true) but if k =3 , then yes k >1. As this statement is not a definite yes or no , this is not a sufficient statement.

Per statement 2, k/2 = integer ---> k = even integer = ...-2,0,2,4,6... etc . So is k<-2 or k>1 can be both yes or no per this statement. Hence this statement is not sufficient.

Combining, we get, k>0 and thus k =2,4,6,8.... ----> (k-1)(k+2) > 0 , a definite yes. Thus, C is the correct answer.

(1) k is an integer greater than zero. (2) k divided by 2 is an integer.

Kudos for a correct solution.

Question : Is k^2 + k – 2 > 0? i.e. Question : Is k^2 - 2k + k – 2 > 0? i.e. Question : Is (k - 2) (k + 1) > 0?

GMATinsight, given equation is k^2+k-1 and not k^2-k+1. The red part above is incorrect.

Made correction, Thank you ...
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(1) k is an integer greater than zero. (2) k divided by 2 is an integer.

Kudos for a correct solution.

800score Official Solution:

The first thing we need to do is factor k² + k – 2 into (k + 2)(k – 1). From these factors, we can see that the value of k² + k – 2 = 0 when k = -2 or 1.

When k > 1, both k + 2 and k – 1 will be positive, so the product of the two (the original expression) will be positive.

Similarly, when k is between -2 and 1, the product of the two expressions will be negative.

Finally, when k is less than -2, the product will be positive.

So we've learned that k² + k – 2 > 0 as long as k is greater than 1 or less than -2.

Statement (1) tells us that k is an integer greater than zero. This is not sufficient because k² + k – 2 > 0 when k is greater than 1, but it will equal zero when k is 1.

Statement (2) tells us k is an even integer. This is also insufficient, because all even integer values of k will make k² + k – 2 greater than zero except -2 and 0. k = -2 will make the expression equal to zero, and k = 0 will make the expression negative. (Remember: 0 is an even integer!)

Combined, the two statements are sufficient, because the only possible values for k are positive even numbers (2 or greater), all of which make k² + k – 2 > 0.

Since the statements are insufficient individually, but sufficient when combined, the correct answer is choice (C). _________________

(1) k is an integer greater than zero. (2) k divided by 2 is an integer.

Kudos for a correct solution.

Target question:Is k² + k – 2 > 0? This is a good candidate for rephrasing the target question.

What needs to happen in order for k² + k – 2 to be positive? Factor to get: k² + k – 2 = (k + 2)(k - 1) For (k + 2)(k - 1) to be positive, we need one of two scenarios:

Scenario A: (k + 2) and (k - 1) are both POSITIVE For this to occur, k must be greater than 1

Scenario B: (k + 2) and (k - 1) are both NEGATIVE For this to occur, k must be less than -2

In other words, for k² + k – 2 to be positive, it must be the case that EITHER k is greater than 1 OR k is less than -2 REPHRASED target question:Is it true that EITHER k is greater than 1, OR k is less than -2?

Once we've rephrased the target question, we can head to the two statements....

Statement 1: k is an integer greater than zero. There are several values of k that satisfy statement 1. Here are two: Case a: k = 2, in which case the answer to the REPHRASED target question is YES Case b: k = 1, in which case the answer to the REPHRASED target question is NO Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: k divided by 2 is an integer There are several values of k that satisfy statement 2. Here are two: Case a: k = 2, in which case the answer to the REPHRASED target question is YES Case b: k = 0, in which case the answer to the REPHRASED target question is NO Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined Statement 1 tells us that k is positive Statement 2 tells us that k divided by 2 is an integer. In other words, k/2 must be a positive integer Some possible values of k: 2, 4, 6, 8, . . . In all of these cases, the answer to the REPHRASED target question is YES Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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