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Is k² + k – 2 > 0?

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Joined: 02 Sep 2009
Posts: 44332
Is k² + k – 2 > 0? [#permalink]

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23 Jul 2015, 03:18
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Is k^2 + k – 2 > 0?

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

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Is k² + k – 2 > 0? [#permalink]

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23 Jul 2015, 03:44
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Bunuel wrote:
Is k^2 + k – 2 > 0?

(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

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Last edited by GMATinsight on 23 Jul 2015, 03:57, edited 2 times in total.
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Joined: 20 Mar 2014
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GMAT 1: 750 Q49 V44
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Re: Is k² + k – 2 > 0? [#permalink]

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23 Jul 2015, 03:48
1
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Bunuel wrote:
Is k^2 + k – 2 > 0?

(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.
Current Student
Joined: 20 Mar 2014
Posts: 2686
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Is k² + k – 2 > 0? [#permalink]

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23 Jul 2015, 03:50
1
KUDOS
GMATinsight wrote:
Bunuel wrote:
Is k^2 + k – 2 > 0?

(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.
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Re: Is k² + k – 2 > 0? [#permalink]

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23 Jul 2015, 03:58
Engr2012 wrote:
GMATinsight wrote:
Bunuel wrote:
Is k^2 + k – 2 > 0?

(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.

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Is k² + k – 2 > 0? [#permalink]

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23 Jul 2015, 06:22
1
KUDOS
Our Question is
$$k^2+k-2>0 ?$$

Restate the given as $$k^2+2k-1k-2>0$$ ------> $$(k-1)(k+2)>0$$ ---------> k > 1 or k > -2

So our question now is Is k>1 or k> -2 ?

Statement 1 --- k > 0

Take k = 1 we get No
k = 2 we get Yes
So Not Sufficient

Statement 2 --- $$\frac{k}{2}$$ = Integer our in other words k can be even

Take k = 2 we get Yes
Take k = -2 we get No
So Not Sufficient

Together 1 + 2 we get
K is even and k > 0

So It is sufficient and answer is C
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Posts: 613
Re: Is k² + k – 2 > 0? [#permalink]

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23 Jul 2015, 06:57
Bunuel wrote:
Is k^2 + k – 2 > 0?

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

Kudos for a correct solution.

Statement 1: k is an integer>0
Given: (k-1)(k+2)>0 ?
Put k=1, equation=0
Put k=2, equation>0. Insufficient

Statement 2: k divided by 2 is an integer. k could be 0,2,4,6 etc
Insufficient

Using both, k =2,4,6 etc.
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Joined: 02 Sep 2009
Posts: 44332
Re: Is k² + k – 2 > 0? [#permalink]

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26 Jul 2015, 12:41
Bunuel wrote:
Is k^2 + k – 2 > 0?

(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).
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Re: Is k² + k – 2 > 0? [#permalink]

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10 Nov 2017, 11:14
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Top Contributor
Bunuel wrote:
Is k^2 + k – 2 > 0?

(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

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Re: Is k² + k – 2 > 0?   [#permalink] 10 Nov 2017, 11:14
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